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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 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.
Original language | English |
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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 | |
Publication status | Published - Feb 2021 |
Bibliographical note
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Dive into the research topics of 'Orlicz–Minkowski flows'. Together they form a unique fingerprint.Projects
- 1 Finished
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Analysis of fully non-linear geometric problems and differential equations
3/01/18 → 2/01/21
Project: Research