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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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

curvature flow anisotropic flow Minkowski problem


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.

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