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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Shankar Venkataramani
University of Arizona
Title: Existence and regularity for solutions to Hyperbolic Monge-Ampere equations with applications to Non-euclidean elasticity

Abstract: I will discuss some recent results on existence/non-existence of solutions to hyperbolic Monge-Ampere equations with various degrees of regularity, with an emphasis on numerical methods for constructing "rough" solutions. I will then discuss some applications of our results to (i) the occurrence of "geometric" defects that are invisible to the energy, but play a crucial role in determining the global morphology, (ii) a generalization of the Sine-Gordon equation to describe "rough" hyperbolic surfaces with constant negative curvature, and (iii) the important role of regularity in quantitative versions of the Hilbert-Efimov theorem on the nonexistence of $C^2$ isometric immersions of the Hyperbolic plane into $R^3$.

This is based on joint work with Toby Shearman and Ken Yamamoto (both at U. Arizona).

Date: Tuesday, September 11, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Acharrya