Orlicz–Minkowski flows

Paul Bryan; Mohammad N. Ivaki; Julian Scheuer

doi:10.1007/s00526-020-01886-3

Orlicz–Minkowski flows

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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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 they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence 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.

Original language	English
Article number	41
Pages (from-to)	1-25
Number of pages	25
Journal	Calculus of Variations and Partial Differential Equations
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/s00526-020-01886-3
Publication status	Published - Feb 2021

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Copyright the Author(s) 2021. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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Cite this

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title = "Orlicz–Minkowski flows",

abstract = "We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence 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.",

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AU - Bryan, Paul

AU - Ivaki, Mohammad N.

AU - Scheuer, Julian

N1 - Copyright the Author(s) 2021. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2021/2

Y1 - 2021/2

N2 - We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence 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.

AB - We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence 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.

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ER -

Orlicz–Minkowski flows

Abstract

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Analysis of fully non-linear geometric problems and differential equations

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Orlicz–Minkowski flows

Abstract

Bibliographical note

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Analysis of fully non-linear geometric problems and differential equations

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