New affine inequalities and projectionmean ellipsoids

Zou Du Wuhan University of Science and Technology Xiong Ge Tongji University

Differential Geometry Geometric Analysis and Geometric Topology Convex and Discrete Geometry mathscidoc:2103.10003

Calculus of Variations and PDEs, 58, (2), 44, 2019
A variational formula for the Lutwak affine surface areas j of convex bodies in Rn is established when 1 ≤ j ≤ n − 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.
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  title={New affine inequalities and projectionmean ellipsoids},
  author={Zou Du, and Xiong Ge},
  booktitle={Calculus of Variations and PDEs},
Zou Du, and Xiong Ge. New affine inequalities and projectionmean ellipsoids. 2019. Vol. 58. In Calculus of Variations and PDEs. pp.44.
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