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In this talk we present a result about a classification of the rotationally-symmetric solutions to an overdetermined problem in the 2-sphere. As a consequence, we give a rigidity result about a certain type of minimal surfaces and as a corollary of this result we provide a new characterization of the critical catenoid among the embedded free boundary minimal annulus in the unit ball. This is based in a join work with José M. Espinar.

Diego A. Marín (Universidad de Granada) An overdetermined problem in the 2-sphere and the critical catenoid conjecture

The so-called Schiffer conjecture was stated by S.T. Yau in his famous list of open problems as follows: If a nonconstant Neumann eigenfunction $u$ of the Laplacian on a smooth bounded domain in $\mathbb{R}^2$ is constant on the boundary, then the domain is a disk. In this talk we will consider a version of such question for domains with disconnected boundary. Specifically, we consider Neumann eigenfunctions that are locally constant on the boundary, and we wonder if the domain has to be necessarily a disk or an annulus. We will show that the answer to the above question is negative. Indeed, there are nonradial Neumann eigenfunctions which are locally constant on the boundary of the domain. The proof uses a local bifurcation argument together with a reformulation of the problem by Fall, Minlend and Weth that avoids a problem of loss of derivatives. This is joint work with A. Enciso, A. J. Fernández and P. Sicbaldi.

David Ruiz (Universidad de Granada) A Schiffer-type problem for annular domains

Rigidity of the grim reaper cylinder as a collapsed self-translating soliton

Mean curvature flow self-translating solitons are minimal hypersurfaces for a certain incomplete conformal background metric, and are among the possible singularity models for the flow. In the collapsed case, they are confined to slabs in space. The simplest non-trivial such example, the grim reaper curve $\Gamma$ in $\mathbb{R}^2$, has been known since 1956, as an explicit ODE-solution, which also easily gave its uniqueness. We consider here the case of surfaces, where the rigidity result for $\Gamma\times\mathbb{R}$ that we'll show this: The grim reaper cylinder is the unique (up to rigid motions) finite entropy unit speed self-translating surface which has width equal to $\pi$ and is bounded from below. (Joint w/ Impera \& Rimoldi.) Time permitting, we'll also discuss recent uniqueness results in the collapsed simply-connected low entropy case (joint w/ Gama \& Martín), using Morse theory and nodal set techniques, which extend Chini's classification.

Niels Martin Moller (University of Copenhagen) Rigidity of the grim reaper cylinder as a collapsed self-translating soliton

Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure

In a recent work with A.Alarcón and I.Castro-Infantes we show that every open Riemann surface admits a complete conformal CMC-1 (constant mean curvature one) immersion in the three dimensional hyperbolic space. In this talk I aim to explain the main ideas in the proof of this result, which relies on the holomorphic representation of CMC-1 surfaces given by Robert Bryant in 1987, and applies modern complex analysis techniques.

Jorge Hidalgo (Universidad de Granada) Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure

Real hypersurfaces with pseudo-Ricci-Bourguignon soliton in the complex two-plane Grassmannians

In this talk, we investigate a pseudo-Ricci-Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$. By using pseudo-anti commuting Ricci tensor, we give a complete classification of Hopf pseudo-Ricci-Bourguignon soliton real hypersurfaces in $G_2({\mathbb C}^{m+2})$ . Moreover, we have proved that there exists a non-trivial classification of gradient pseudo-Ricci-Bourguignon soliton $(M, {\xi}, {\eta}, {\Omega}, {\theta}, {\gamma}, g)$ on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$. In the class of contact hypersurface in $G_2({\mathbb C}^{m+2})$, we prove that there does not exist a gradient pseudo-Ricci-Bourguignon soliton in $G_2({\mathbb C}^{m+2})$

Changhwa Woo (Pukyong National University) Real hypersurfaces with pseudo-Ricci-Bourguignon soliton in the complex two-plane Grassmannians

Yamabe, Ricci-Bourguignon solitons in complex hyperbolic quadric and complex hyperbolic space

In this talk, we give a complete classification of Yamabe soliton, Ricci-Bourguignon soliton on real hypersurfaces in complex hyperbolic quadric ${Q^m}^*$ and complex hyperbolic space $CH^m$. Next as applications, we also give a complete classification of gradient Yamabe soliton and gradient Ricci-Bourguignon soliton on real hypersurfaces in complex hyperbolic quadric ${Q^m}^*$ and complex hyperbolic space $CH^m$. Related to this topics, finally we want to mention soliton problems and Fisher-Marsden conjecture in other Hermitian symmetric spaces like complex two-plane Grassmannians, complex hyperbolic two-plane Grassmannians, complex quadric or etc.

Young Jin Suh (Kyungpook National University) Yamabe, Ricci-Bourguignon solitons in complex hyperbolic quadric and complex hyperbolic space

A smooth function $f$ on a Riemannian manifold $\widetilde{M}$ is isoparametric if $|\nabla f|$ and $\Delta f$ are constant on the level sets of $f$. A hypersurface $M \subset \widetilde{M}$ is an isoparametric hypersurface if it is a regular level set of an isoparametric function defined on $\widetilde{M}$. When the ambient space is a space form $\mathbb{Q}^{n}_c$, the definition of isoparametric hypersurface is equivalent to saying that the hypersurface has constant principal curvatures. However, in arbitrary ambient spaces of nonconstant sectional curvature, the equivalence between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures may no longer be true. In this talk, it will be presented characterization and classification results on isoparametric hypersurfaces with constant principal curvatures in the product spaces $ \mathbb{Q}_{c_{1}}^2 \times \mathbb{Q}_{c_{2}}^2$, for $c_{i} \in \{-1,0,1\}$ and $c_1 \neq c_2$. The talk is based on a joint work with Jo$\tilde{\rm a}$o Batista Marques dos Santos.

João Paulo dos Santos (Universidade de Brasilia) Isoparametric hypersurfaces in product spaces

The moduli space of solutions to Nahm’s equations with values in the Lie algebra of a Lie group G (more generally, self-dual Yang-Mills equations) carries a complete hyperkähler structure, obtained via infinite-dimensional reduction by Hitchin (1987). Kronheimer (1989) proved that this is diffeomorphic to the total space of the cotangent bundle T*Gc of a complex Lie group. Both the hyperkähler structure on the moduli space and the diffeomorphism with T*Gc are proved to exist abstractly; hence, the resulting hyperkähler metric on T*Gc is challenging to describe explicitly even for basic Lie groups. We present joint work with Richard Melrose and Michael Singer obtaining the asymptotics of the metric on the moduli space and the resolution of the critical set of the Nahm vector. We also present an explicit description of the diffeomorphism and induced metric on T* in the case of G=SU(2).

Raphael Tsiamis (Columbia University) The hyperkähler metric on T*SL(2,C)

Gap results for free boundary CMC surfaces in certain spaces

One of the most extensively studied topics in Differential Geometry is minimal surfaces. This subject has connections with a wide range of mathematics areas, such as complex analysis, partial differential equations and topology. A classic problem in this context is the Plateau problem and recently much attention has been given to problems with the free boundary condition. In this talk, we will present some results about classification for constant mean curvature (CMC) surfaces with the free boundary condition in certain spaces. This is a joint work with Ezequiel Barbosa (UFMG) and Edno Pereira (UFSJ).

Maria Andrade (Universidade Federal de Sergipe) Gap results for free boundary CMC surfaces in certain spaces

In 1841 Delaunay characterized surfaces of constant mean curvature $H=1$ in Euclidean 3-space invariant under rotation. The result was generalized by several authors to screw-motion invariant CMC surfaces in $\mathbb{E}(\kappa,\tau)$. In this more general setting CMC tubes can arise in addition to the Delaunay surfaces. In this talk I want to present existence conditions and talk about further properties of these tubes such as embeddedness and foliation.

Philipp Käse (Technische Universität Darmstadt) CMC tubes in homogeneous spaces

In this talk, we will consider an arbitrary orientable Riemannian surface $M$ and an open relatively compact domain $\Omega\subset M$ with piecewise regular boundary. Given a Killing submersion $\pi:\mathbb{E}\to M$, we will discuss some properties of the divergence lines spanned by a sequence of minimal graphs over $\Omega$, as well as how they produce certain laminations in $\pi^{-1}(\Omega)$ whose leaves are vertical surfaces (after considering a subsequence). We will apply these results to give a general solution to the Jenkins-Serrin problem over $\Omega$ under natural necessary assumptions. This is a joint work with Andrea del Prete and Barbara Nelli.

José M. Manzano (Universidad de Jaén) On the convergence of minimal graphs

A generalised Picone identity of $p(x)$-sub-Laplacian for general vector fields and applications

Picone identity named after Mauro Picone (1885-1977) is classical in the theory of homogeneous linear second order differential equations yielding many results. In this talk, I will present a new generalised variable exponent Picone type identity for horizontal $p(x)$-Laplacian of general vector fields. The identity generalises several known results in literature. Then as an application, we will study the indefinite weighted Dirichlet eigenvalue problem for horizontal $p(x)$-sub-Laplacian on smooth manifolds and discuss some properties of the first eigenvalue and its corresponding eigenfunctions such as uniqueness, simplicity, monotonicity and isolation in the context of variable exponent Sobolev spaces. Further applications also yield Hardy type inequalities and Caccioppoli estimates with variable exponent.

Abimbola Abolarinwa (University of Lagos) A generalised Picone identity of $p(x)$-sub-Laplacian for general vector fields and applications

Determine homotopy classes by the mean curvature flow

A map is said to be homotopic equivalent to another map if there is a continuous path of maps connecting the two. Surprisingly a geometric flow such as the mean curvature flow provides natural paths to deform a map to a canonical representative in its homotopy class. I shall discuss this approach and its applications, and in particular some recent results regarding the homotopy class of maps between complex projective spaces of different dimensions. This is based on joint work with Chun-Jun Tsai and Mao-Pei Tsui.

Mu Tao Wang (Columbia University) Determine homotopy classes by the mean curvature flow

Complete meromorphic curves with Jordan boundaries

We prove that given a finite set $E$ in a bordered Riemann surface $\mathcal{R}$, there is a continuous map $h\colon \overline{\mathcal{R}}\setminus E\to\mathbb{C}^n$ ($n\geq 2$) such that $h|_{\mathcal{R}\setminus E} \colon \mathcal{R}\setminus E\to\mathbb{C}^n$ is a complete holomorphic immersion (embedding if $n\geq 3$) which is meromorphic on $\mathcal{R}$ and has effective poles at all points in $E$, and $h|_{b\overline{\mathcal{R}}} \colon b\overline{\mathcal{R}}\to\mathbb{C}^n$ is a topological embedding. In particular, $h(b\overline{\mathcal{R}})$ consists of the union of finitely many pairwise disjoint Jordan curves which we ensure to be of Hausdorff dimension one. We establish a more general result including uniform approximation and interpolation.

Tjaša Vrhovnik (Universidad de Granada) Complete meromorphic curves with Jordan boundaries

"International Workshop on Geometry of Submanifolds, 2023" will be held at Science Faculty of Istanbul University in Vezneciler-Fatih, Istanbul, Türkiye during 6-8 November 2023 and it will be dedicated to Cem Tezer (1955-2020) who was one of the members of the Scientific Committee of "International Workshop on Geometry of Submanifolds, 2019" held at Istanbul Center for Mathematical Sciences (IMBM) located in Boğaziçi University South Campus in Bebek, Istanbul, Türkiye during 7-9 November 2019. The purpose of the workshop is to bring experts and young researchers working in various aspects of "Geometry of Submanifolds" together to create an environment where they can discuss about their recent research and open problems. This workshop is supported by TMD MAD fund of Turkish Mathematical Society (TMD).

Geometric PDE's Day

Granada (España)

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Seminar 2 10:30 — 11:30 Niels M. Moller (University of Copenhagen) 12:00 — 13:00 David Ruiz (University of Granada) Break for lunch. 16:00 — 17:00 Eddygledson Souza Gama (Universidade Federal de Pernambuco)

The aim of the workshop is to focus on different recent advances in differential geometry and its applications, with particular emphasis on Riemannian, metric and global differential geometry, theory of submanifolds and geometric flows.

The Hermann Minkowski Meetings on the Foundations of Spacetime Physics, organized by the Minkowski Institute, bring together experts on spacetime physics and its foundations. The Scientific Organizing Committee hopes that these meetings will become one of the preferred biennial forums for reporting research results and having fruitful discussions with colleagues. The Third Hermann Minkowski Meeting on the Foundations of Spacetime Physics will commemorate the 115th anniversary of Minkowski's 1908 world-view-changing lecture "Space and Time," which presented the novel ideas of the spacetime structure of the world and the four-dimensional physics of spacetime. In addition to technical papers on spacetime physics, papers on closely related topics, including on conceptual issues of spacetime physics, will be also welcome.

The Fall Workshops on Geometry and Physics have been held yearly since 1992, and bring together Spanish and Portuguese geometers and physicists, along with an ever increasing number of participants from outside the Iberian Peninsula. The meetings aim to provide a forum for the exchange of ideas between researchers of different fields in Differential Geometry, Applied Mathematics and Physics, and always include a substantial number of enthusiastic young researchers amongst the participants.

The PADGE conferences are organized approximately every five years and usually attract a good audience of differential geometers from all over the world. This year's edition is dedicated to the memory of Franki Dillen, geometry professor at KU Leuven, who passed away 10 years ago.

The Nordic Congress of Mathematicians is held usually once every four years under the auspices of the national mathematical associations of Denmark, Finland, Iceland, Norway, and Sweden. The 29th Nordic Congress of Mathematicians, in collaboration with the European Mathematical Society, will be held at Aalborg University, Denmark. It marks the 150th anniversary of the Danish Mathematical Society whose foundation dates back to 1873. Nine eminent mathematicians from a diversity of mathematical areas will promote our subject through plenary talks that will take place in Aalborg’s majestic Music Hall located on the Limfjord waterfront. A five-minute walk leads to a modern university building that hosts a substantial number of parallel session meetings, organized bottom-up, including a poster session.

We would like to invite everyone to the Conference on Complex Analysis and Geometry -- Celebrating the 70+1th birthday of Laszlo Lempert. The conference will be held in the Erdos Center of the Renyi Institute in Budapest in the week of June 26-30, 2023.

Este seminario de 10 horas está dirigido al alumnado del Programa Interuniversitario Matemáticas (UGR, UCA, UMA, UAL y UJA), aunque la inscripción está abierta a cualquier persona interesada en asistir. El objetivo de esta actividad es transmitir de manera clara y fluida avances en los problemas recientes de investigación básica en análisis geométrico, una de las líneas de investigación del programa de doctorado. El seminario consta de 5 minicursos de 2 horas de duración impartidos por profesorado experto en el área.

The goal is to bring together leading researchers worldwide in complex analysis, geometry, and dynamics, with the aim of enhanced future collaboration. These fields are strongly interrelated, and in order to be able to solve deep challenging problems it is becoming necessary to pursue synergies among them to a bigger degree than in the past.

The broad finality of the meeting is to gather together leading experts in various fields of geometric analysis to give an up-to-date description of the state of the art and the recent important developments in the field. Special attention will be devoted to the role of PDE theory.

Conference topics include Spectral Geometry, Shape Optimization, Minimal Surface Theory and Isoperimetric Problems.

The Young Researchers Workshop in Geometry, Mechanics, and Control is a yearly event to promote young researchers in the field of differential geometry and its relations to mechanics and control theory. The 17th edition takes place in Leuven, Belgium. The workshop features three mini-courses in key topics in the field, selected talks proposed by the participants and a session with 5-to-10-minutes presentations. This event is targeted to all researchers in the field, with an emphasis on young participants (doctoral students and postdocs).

Constant mean curvature surfaces and related areas of submanifold theory represent a classical field of research that uses techniques from both Differential Geometry and Geometric Analysis. The aim of this $\mathcal{H}$-workshop is to gather together some distinguished geometers to discuss some cutting-edge discoveries in this field, as well as to give PhD students the opportunity to present their works. This event has been conceived as part of the project constant mean curvature surfaces in homogeneous 3-manifolds, supported by MICIN/AEI grant PID2019-111531GA-I00.

El VI Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española se organiza en la Universidad de León del 6 al 10 de Febrero de 2023. Tras la buena acogida de pasadas ediciones (Soria (2011), Sevilla (2013), Murcia (2015), Valencia (2017) y Castellón (2019)), se desea que esta nueva edición siga siendo un lugar de encuentro de jóvenes matemáticos donde poder intercambiar ideas, conocer investigadores de otras universidades y establecer contactos que puedan ser productivos y perdurar en el tiempo.