Peter McGrath - Quantitative Isoperimetric Inequalities on Riemannian Surfaces

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.