A flow approach to the $L_{-2}$ Minkowski problem

Abstract

We prove that the set of smooth, $\pi$-periodic, positive functions on the unit circle for which the $L_{-2}$ Minkowski problem is solvable is dense in the set of all smooth, $\pi$-periodic, positive functions on the unit circle with respect to the $L^{\infty }$ norm. Furthermore, we obtain a necessary condition on the solvability of the even $L_{-2}$ Minkowski problem. At the end, we prove uniqueness of the solutions up to an affine linear transformation.

to appear in Adv. Appl. Math, fixed some typos

References in corpus (1)

• The Logarithmic Minkowski Problem

Cited by in corpus (1)

• Affine-geometric Wirtinger inequality