The University of Arizona

Some variational problems for surfaces with negative curvature

Some variational problems for surfaces with negative curvature

Series: Analysis, Dynamics, and Applications Seminar
Location: Math 402
Presenter: Shankar Venkataramani, Department of Mathematics, University of Arizona

I will talk about some recent progress on "optimal" isometric embeddings of surfaces with negative curvature into R^3. Some of the results include (i) a generalization of the Sine-Gordon equation to describe “rough” hyperbolic surfaces with constant negative curvature, and (ii) the important role of regularity in quantitative versions of the Hilbert-Efimov theorem on the nonexistence of isometric immersions of the Hyperbolic plane into R^3 . This is joint work with Toby Shearman

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