Parabolic approaches to curvature equations

Bryan, Paul, Ivaki, Mohammad N. and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2021. Parabolic approaches to curvature equations. Nonlinear Analysis: Theory, Methods and Applications 203 , 112174. 10.1016/j.na.2020.112174

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Abstract

We employ curvature flows without global terms to seek strictly convex, spacelike solutions of a broad class of elliptic prescribed curvature equations in the simply connected Riemannian spaceforms and the Lorentzian de Sitter space, where the prescribed function may depend on the position and the normal vector. In particular, in the Euclidean space we solve a class of prescribed curvature measure problems, intermediate Lp-Aleksandrov and dual Minkowski problems as well as their counterparts, namely the Lp-Christoffel-Minkowski type problems. In some cases we do not impose any condition on the anisotropy except positivity, and in the remaining cases our condition resembles the constant rank theorem/convexity principle due to Caffarelli-Guan-Ma (Commun. Pure Appl. Math. 60 (2007), 1769--1791). Our approach does not rely on monotone entropy functionals and it is suitable to treat curvature problems that do not possess variational structures.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0362-546X
Date of First Compliant Deposit:	18 October 2020
Date of Acceptance:	18 October 2020
Last Modified:	08 Nov 2023 09:19
URI:	https://orca.cardiff.ac.uk/id/eprint/135712

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