Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact 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, 2018Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  Acharrya