Smoothness in the $l_p$ Minkowski problem for $p<1$

Abstract

We discuss the smoothness and strict convexity of the solution of the $L_p$ Minkowski problem when $p<1$ and the given measure has a positive density function.

References in corpus (2)

• The Logarithmic Minkowski Problem
• A probabilistic approach to the geometry of the \ell_p^n-ball

Cited by in corpus (8)

• The $L_p$-Minkowski problem for $-n<p<1$
• Orlicz-Minkowski flows
• The Orlicz version of the $L_p$ Minkowski problem on $S^{n-1}$ for $-n<p<0$
• Parabolic approaches to curvature equations
• $L^p$-Minkowski Problem under Curvature Pinching
• Iterations of curvature images
• Curvature bound for $L_p$ Minkowski problem
• Diameter estimate for planar $L_p$ dual Minkowski problem