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

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.

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