Projection Body and Isoperimetric Inequalities for s-Concave Functions

摘要

For a positive integer s, the projection body of an s-concave function f : R-n ? [0, +8), a convex body in the (n + s)-dimensional Euclidean space Rn+s, is introduced. Associated inequalities for s-concave functions, such as, the functional isoperimetric in-equality, the functional Petty projection inequality and the functional Loomis-Whitney inequality are obtained.

关键词