## New Monotone Quantities along Inverse Curvature Flows and Minkowski Type Formulas

Dr. Kwok-Kun Kwong

(Miami)

Abstract

Monotone quantities along hypersurfaces evolving under the inverse mean curvature flow have many applications in geometry and relativity. In this talk, I will discuss a family of new monotone increasing quantities along inverse curvature flows in the Euclidean space. I will also discuss a related Minkowski type formula and a geometric inequality for closed hypersurfaces with positive k-th mean curvature. This is joint work with Pengzi Miao.