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# Jenkins-Serrin problem for translating graphs

I will discuss about recent joint works with E.S. Gama, J. de Lira and F. Martín concerning Jenkins-Serrin type problems for the graphical translators of the mean curvature flow in Riemannian product manifolds $M\times R$. We prove, for example, the existence of Jenkins-Serrin type translators that can be described as horizontal graphs "over" suitable domains in a vertical plane.

# Some results of invariant theory for CR-manifolds

## Yen-Chang Huang Xinyang Normal University

In this talk, I will introduce some recent works of invariant theory on CR manifolds. After a briefing of CR manifolds, some integral invariants will be introduced in the Heisenberg groups (regarded as a flat model of CR manifolds). The invariants are not changed in the sense of the pseudo-hermitian transformations which can be regarded as the rigid motions in the Heisenberg groups. We take the approach from Integral Geometry for convex bodies, but in our case, the assumption of convexity is not necessary. The applications can be implemented to the CR-version of the Crofton's formula and the containment problems with other related. Some recent development in the invariant theory for CR manifolds will also be discussed in the end of the talk.

Seminario 1ª planta, IEMath-GR

# Isoparametric surfaces in $\mathbb{E}(\kappa,\tau)$-spaces

## José M. Manzano Universidad Complutense de Madrid

We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group:

• isoparametric surfaces,
• surfaces with constant principal curvatures,
• extrinsically homogeneous surfaces,
• $H$-surfaces with vanishing Abresch-Rosenberg differential.
This is a joint work with Miguel Domínguez Vázquez.

Seminario 1ª planta, IEMath-GR

# Carleman type theorems in complex analysis and minimal surface theory

## Brett Chenoweth Universidad de Liubliana

Carleman’s approximation theorem (1927) was ostensibly the first result concerning approximation of continuous functions defined on an unbounded closed set of C, namely R, by entire functions. The approximation is stronger than uniform approximation as the error at x can be made to taper off as x approaches infinity (from within R). An essential property of R for such an approximation to exist is that it has bounded exhaustion hulls, that is, the complement of R in the one point compactification of C is locally connected at infinity. Bounded exhaustion hulls play an important role in the characterisation of totally real sets admitting Carleman approximation and Carleman approximation of jets; see Manne et al (2011), Magnusson and Wold (2016). In this talk I will discuss some recent generalisations of Carleman’s theorem including preliminary results from ongoing joint work with Ildefonso Castro-Infantes where the problem of approximating by directed holomorphic immersions, for example by null curves, is being considered.

Seminario de la primera planta, IEMath

# IX Workshop on Differential Geometry

## Maceió (Brazil)

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The Workshop on Differential Geometry of the Institute of Mathematics of the Federal University of Alagoas has become a traditional event that takes place every year in Maceio-Alagoas, during the Brazilian summer. The aim of this workshop is to gather in Maceio national and international researchers of high scientific level in the field of differential geometry. In this 9th edition, the event will be held in two weeks. From 11 to 15 March, the activities will occur on the Mathematics Institute of the Federal University of Alagoas, and the program is dedicated to young researchers and graduate students, including a minicourse, 30min contributed talks and two sections of open problems. From 18 to 22 March, the activities will occur at Hotel Ponta Verde at Praia do Francês and keeps the traditional program with one minicourse and invited lectures.

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