The $L_p$-Minkowski problem for $-n<p<1$

Abstract

Chou and Wang's existence result for the $L_p$-Minkowski problem on ${\mathbb{S}}^{n-1}$ for $p\in (-n,1)$ and an absolutely continuous measure $\mu$ is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case $p\in (0,1)$.

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Cited by in corpus (11)

• The Orlicz version of the $L_p$ Minkowski problem on $S^{n-1}$ for $-n<p<0$
• Orlicz-Minkowski flows
• Parabolic approaches to curvature equations
• On the uniqueness of solutions to the isotropic $L_p$ dual Minkowski problem
• $L^p$-Minkowski Problem under Curvature Pinching
• Iterations of curvature images
• Curvature bound for $L_p$ Minkowski problem
• A non-existence result for the $L_p$-Minkowski problem
• Prescribed $L_p$ curvature problem
• The Minkowski problem in the Gaussian probability space
• A flow method to the Orlicz-Aleksandrov problem