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arXiv · 2005.00143

Orlicz-Minkowski flows

Paul Bryan·Mohammad N. Ivaki·Julian Scheuer
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Abstract

We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if exist, solve the regular Orlicz-Minkowski problems. As an application, we obtain old and new results for the regular even Orlicz-Minkowski problems; the corresponding $L_p$ version is the even $L_p$-Minkowski problem for $p>-n-1$. Moreover, employing a parabolic approximation method, we give new proofs of some of the existence results for the general Orlicz-Minkowski problems; the $L_p$ versions are the even $L_p$-Minkowski problem for $p>0$ and the $L_p$-Minkowski problem for $p>1$. In the final section, we use a curvature flow with no global term to solve a class of $L_p$-Christoffel-Minkowski type problems.

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BibTeXRIS

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer. 2020-04-30. Orlicz-Minkowski flows. https://doi.org/10.1007/s00526-020-01886-3

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