Vol. 249, No. 2, 2011

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A gluing construction for prescribed mean curvature

Adrian Butscher

Vol. 249 (2011), No. 2, 257–269
Abstract

The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respect to the prescribed mean curvature function.

Keywords
gluing constructions, prescribed mean curvature
Mathematical Subject Classification 2000
Primary: 53A10, 58J05
Milestones
Received: 28 May 2009
Revised: 7 September 2010
Accepted: 10 November 2010
Published: 1 February 2011
Authors
Adrian Butscher
Department of Mathematics
Stanford University
Stanford, CA 94305
United States