11/10/2006

Gaoyong Zhang
Polytechnic University, NY

An L_p Affine Isoperimetric Inequality and Its Applications

Affine surface areas of convex bodies will be defined by an integral geometric approach. An L_p affine isoperimetric inequality that is stronger than the classical isoperimetric inequality will be discussed. The affine isoperimetric inequality can be applied to establishing sharp affine Sobolev inequalities. This strengthens the equivalence of the isoperimetric inequality and the sharp Sobolev inequality.