Peter McGrath - Quantitative Isoperimetric Inequalities on Riemannian Surfaces

Tuesday, September 1, 2020 - 13:00
Speaker Information
Peter McGrath
North Carolina State University

Abstract or Additional Information

In this talk, we introduce a scattering asymmetry which measures the asymmetry of a domain by quantifying its incompatibility with an isometric circle action.  We prove a quantitative isoperimetric inequality involving the scattering asymmetry and characterize the domains with vanishing scattering asymmetry by their rotational symmetry.  We also give a new proof of the sharp Sobolev inequality for Riemannian surfaces which is independent of the isoperimetric inequality.  This is joint work with J. Hoisington.

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