No abstract uploaded!

No abstract uploaded!

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.

Existence and uniqueness of the solution to the Lp Minkowski problem for the electrostatic p-capacity are proved when p > 1 and 1 < p < n. These results are nonlinear extensions of the very recent solution to the Lp Minkowski problem for p-capacity when p = 1 and 1 < p < n by Colesanti et al. and Akman et al., and the classical solution to the Minkowski problem for electrostatic capacity when p = 1 and p = 2 by Jerison.

No abstract uploaded!