New affine inequalities and projection mean ellipsoids

作者:Zou, Du; Xiong, Ge*
来源:Calculus of Variations and Partial Differential Equations, 2019, 58(2): 44.
DOI:10.1007/s00526-019-1497-0

摘要

A variational formula for the Lutwak affine surface areas j of convex bodies in Rn is established when 1jn-1. By using introduced new ellipsoids associated with projection functions of convex bodies, we prove a sharp isoperimetric inequality for j, which opens up a new passage to attack the longstanding Lutwak conjecture in convex geometry.