Mass and geometric inequalities

Guofang Wang (Freiburg)

Abstract: In this talk, we first use the Gauss-Bonnet-Chern
scalar curvature to introduce a new mass,
Gauss-Bonnet-Chern mass,  for asymptotically flat manifolds
and for asymptotically hyperbolic manifolds. Then we
establish optimal isoperimetric type inequalities to prove
 a Penrose  inequality for this new mass, for a  class of
graphical manifolds. 

(This is a joint work with Yuxin Ge and Jie Wu)