A Gluing Construction for Prescribed Mean Curvature

Details A Gluing Construction for Prescribed Mean Curvature A Gluing Construction for Prescribed Mean Curvature

2009-02-20

arxiv.org/abs/0902.3499v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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 the prescribed mean curvature function.

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