A remark on the existence of sphere with prescribed mean curvature
type: Item
instance of: scholarly article
title: A remark on the existence of sphere with prescribed mean curvature
zbMATH Open document ID: 0898.53005
published in: The Asian Journal of Mathematics
publication date: 1998-11-02T00:00:00Z
review text: In 1976, the author posed the following question: if \(\rho\) is a function defined on \(\mathbb{R}^3\), what is the condition on \(\rho\) so that there is a sphere in \(\mathbb{R}^3\) whose mean curvature is given by \(\rho\). This note gives a new partial solution to the above problem. Using his earlier paper (with R. Schoen) on the existence of black holes (see \textit{R. Schoen} and \textit{S.-T. Yau} [Commun. Math. Phys. 90, 575-579 (1983; Zbl 0541.53054)]), the author solves the prescribed mean curvature problem for a large class of \(\rho\).
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1143928
zbMATH Keywords: Euclidean 3-space
zbMATH Keywords: spheres with prescribed mean curvature
author: Shing-Tung Yau
reviewed by: Marian Hotloś
MaRDI profile type: Publication
DOI: 10.4310/AJM.1997.V1.N2.A6
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description: scientific article; zbMATH DE number 1143928