Uniqueness Theorems for Fully Nonlinear Conformal Equations on Subdomains of the Sphere


Marcos Petrúcio de Almeida Cavalcante

16:00:00 - 17:00:00

R440 , Astronomy and Mathematics Building

In this talk we extend Escobar's classification result [E] to elliptic fully nonlinear conformal equations on certain subdomains of the sphere with prescribed constant mean curvature on its boundary. Such subdomains are the hemisphere with prescribed constant mean curvature on its boundary, and annular domains with minimal boundary. This is joint work with Jose Espinar (IMPA).
[E] J. F. Escobar, Uniqueness theorems on conformal deformation of metrics, Sobolev inequalities, and an eigenvalue estimate.  Comm. Pure Appl. Math. 43 (1990), no. 7, 857--883.