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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Jeffrey Case
Penn State
Title: Some results on a fully nonlinear boundary value problem from conformal geometry

Abstract: A natural problem in geometry is to conformally deform a metric to one for which the k-th elementary symmetric function of the eigenvalues of the Schouten tensor is constant; as a problem in PDE, this is a fully nonlinear second-order PDE. In this talk, I will describe an existence and uniqueness result for the Dirichlet problem by minimizing a certain conformally invariant energy functional. Using similar ideas, I will describe a uniqueness theorem for a related Neumann problem which is closely related to the Sobolev trace embedding. If time allows, I will discuss generalizations to other fully nonlinear second-order operators. This is joint work with Yi Wang.

Date: Thursday, November 30, 2017
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice