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Talks by Graham Andrew Smith

Clifford structures constant extrinsic curvature surfaces

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)

Constant extrinsic curvature surfaces in space forms are best understood as Sasakian objects living in the unitary bundle. In this framework they become bilegendrian surfaces. We discuss the insights this perspective provides on the study of constant extrinsic curvature surfaces.

G11 (Facultad de Ciencias)

The Kulkarni-Pinkall form and locally strictly convex immersions in \(\mathbb{H}^3\)

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)

Watch the talk in youtube

In this talk we study applications of the Kulkarni-Pinkall form to the study of locally strictly convex immersions in \(\mathbb{H}^3\). We deduce a new a priori estimate which in turn allows us to completely solve the asymptotic Plateau problem for \(k\)-surfaces in hyperbolic space as formulated by Labourie. This work has interesting intersections with a paper of Espinar-Gálvez-Mira. This work appears in https://arxiv.org/abs/2104.03181.

Degree Theory of Immersed Submanifolds

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)

In arXiv:1010.1879 we construct an integer valued degree theory for compact, immersed hypersurfaces of constant curvature in general Riemannian manifolds, and we show how this degree theory may be used to prove existence results such hypersurfaces. Joint work with Harold Rosenberg.

Seminario de Matemáticas, 1ª Planta Sección de Matemáticas

Barrier techniques in the non-linear Plateau problem

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)

We show how barrier techniques are used to solve the Plateau problem for general curvature functions in general manifolds.
arXiv:1008.3545

Seminario de Matemáticas, 1ª Planta Sección de Matemáticas

Non-linear Dirichlet problems in Hadamard manifolds

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)

We prove the existence of constant curvature hypersurfaces in Hadamard manifolds subject satisfying topological/boundary conditions.

k-Surfaces and Pseudo-Holomorphic Curves

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)

We discuss how the theory of pseudo-holomorphic curves may be used to study constant Gaussian curvature surfaces in three dimensional manifolds.

Seminario de Matemáticas. 2ª Planta, sección de Matemáticas.

Graham Andrew Smith

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio) (Brasil)

Number of talks
6
Number of visits
4
Last visit

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