PDE Seminar Abstracts

Weighted isoperimetric inequalities in warped product manifolds

Kwok-Kun Kwong
University of Sydney
Mon 8th Oct 2018, 2-3pm, Carslaw Room 829 (AGR)

Abstract

The classical isoperimetric inequality states that among all the closed curves enclosing the same area on the plane, the circle has the smallest perimeter. It has been generalized to hypersurfaces in higher dimensional Euclidean space, and to various ambient spaces. In this talk, I will use the Jensen’s inequality to give a simple proof of some sharp weighted or unweighted isoperimetric type inequalities in warped product manifolds (or more generally multiply warped product manifolds). I will also give some generalizations involving the higher order mean-curvatures. Finally some applications such as eigenvalue estimates, Polya-Szegö type inequality, and Sobolev type inequality, will be given.