Vol. 12, No. 2, 2019

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

Paul Bryan, Mohammad N. Ivaki and Julian Scheuer

Vol. 12 (2019), No. 2, 259–280
DOI: 10.2140/apde.2019.12.259
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 Lp-Minkowski problems in n+1 for p > n 1.

Keywords
curvature flow, anisotropic flow, Minkowski problem
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 35K55, 52A05, 53A15, 58J35
Milestones
Received: 9 August 2016
Accepted: 1 May 2018
Published: 14 August 2018
Authors
Paul Bryan
Department of Mathematics
Macquarie University
Sydney
Australia
Mohammad N. Ivaki
Department of Mathematics
University of Toronto
Toronto, ON
Canada
Julian Scheuer
Mathematisches Institut
Albert-Ludwigs-Universität
Freiburg
Germany