Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 2 (2019), 259-280.

A unified flow approach to smooth, even $L_p$-Minkowski problems

Paul Bryan, Mohammad N. Ivaki, and Julian Scheuer

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Abstract

We study long-time existence and asymptotic behavior for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of smooth, even L p -Minkowski problems in n + 1 for p > n 1 .

Article information

Source
Anal. PDE, Volume 12, Number 2 (2019), 259-280.

Dates
Received: 9 August 2016
Accepted: 1 May 2018
First available in Project Euclid: 9 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.apde/1539050438

Digital Object Identifier
doi:10.2140/apde.2019.12.259

Mathematical Reviews number (MathSciNet)
MR3861892

Zentralblatt MATH identifier
06974514

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35K55: Nonlinear parabolic equations 52A05: Convex sets without dimension restrictions 53A15: Affine differential geometry 58J35: Heat and other parabolic equation methods

Keywords
curvature flow anisotropic flow Minkowski problem

Citation

Bryan, Paul; Ivaki, Mohammad N.; Scheuer, Julian. A unified flow approach to smooth, even $L_p$-Minkowski problems. Anal. PDE 12 (2019), no. 2, 259--280. doi:10.2140/apde.2019.12.259. https://projecteuclid.org/euclid.apde/1539050438


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