Orlicz-Minkowski flows

Bryan, Paul, Ivaki, Mohammad N. and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2021. Orlicz-Minkowski flows. Calculus of Variations and Partial Differential Equations 60 , 41. 10.1007/s00526-020-01886-3

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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 Lp version is the even Lp-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 Lp versions are the even Lp-Minkowski problem for p>0 and the Lp-Minkowski problem for p>1. In the final section, we use a curvature flow with no global term to solve a class of Lp-Christoffel-Minkowski type problems.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publisher:	Springer Verlag
ISSN:	0944-2669
Date of First Compliant Deposit:	14 October 2020
Date of Acceptance:	30 September 2020
Last Modified:	05 May 2023 22:35
URI:	https://orca.cardiff.ac.uk/id/eprint/135618

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