Foliation by free boundary constant mean curvature leaves

2019/04/26 by Montenegro, J. Fabio
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.11867

Abstract

Let M be a Riemannian manifold of dimension n+1 with smooth boundary and p∈ ∂ M. We prove that there exists a smooth foliation around p whose leaves are submanifolds of dimension n, constant mean curvature and its arrive perpendicular to the boundary of M, provided that p is a nondegenerate critical point of the mean curvature function of ∂ M.

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• Constant k-curvature hypersurfaces in Riemannian manifolds
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• Foliations by constant mean curvature tubes
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