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.