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- W4366999728 abstract "We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure $mu$ with a positive smooth density $f$, any solution to the $L_p$ Minkowski problem in $mathbb{R}^{n+1}$ with $p le -n+2$ is a hypersurface of class $C^{1,1}$. This is a sharp result because for each $pin [-n+2,1)$ there exists a convex hypersurface of class $C^{1,frac{1}{n+p-1}}$ which is a solution to the $L_p$ Minkowski problem for a positive smooth density $f$. In particular, the $C^{1,1}$ regularity is optimal in the case $p=-n+2$ which includes the logarithmic Minkowski problem in $mathbb{R}^3$." @default.
- W4366999728 created "2023-04-27" @default.
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- W4366999728 date "2023-04-23" @default.
- W4366999728 modified "2023-09-30" @default.
- W4366999728 title "Curvature bound for $L_p$ Minkowski problem" @default.
- W4366999728 doi "https://doi.org/10.48550/arxiv.2304.11617" @default.
- W4366999728 hasPublicationYear "2023" @default.
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