McGill University

Tue 25 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012

Curvature flows and the isoperimetric problems in geometry

ESB2012
Tue 25 Oct 2016, 3:30pm4:30pm
Abstract
Abstract: We will discuss two types of curvature flows designed to prove isoperimetric type inequalities. The first one is a mean curvature type flow, it was introduced in a previous joint work with Junfang Li in space forms. In a recent joint paper with Junfang Li and MuTao Wang, we consider a similar normalized hypersurface flow in the more general ambient setting of warped product spaces with general base. Under a natural necessary condition, the flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. Under another condition with is related to the notion of “photon sphere” in general relativity, we establish the regularity and convergence of the flow, thereby solve the isoperimetric problem in warped product spaces. In a similar spirit, I will discuss a inverse mean curvature type flow in hyperbolic space to deal with AlexandrovFenchel type isoperimetric inequalities.
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University of Oregon

Tue 1 Nov 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Minimal hypersurfaces with free boundary and positive scalar curvature

ESB 2012
Tue 1 Nov 2016, 3:30pm4:30pm
Abstract
There is a wellknown technique due to SchoenYau from the late 70s which uses (stable) minimal hypersurfaces to find topological implications of a (closed) manifold's ability to support positive scalar curvature metrics. In this talk, we describe a version of this technique for manifolds with boundary and discuss how it can be used to study bordisms of positive scalar curvature metrics.
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Stanford University

Tue 8 Nov 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012


ESB 2012
Tue 8 Nov 2016, 3:30pm4:30pm
Abstract
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