Constant $k$-curvature hypersurfaces in Riemannian manifolds

Details Constant $k$-curvature hypersurfaces in Riemannian manifolds Constant $k$-curvature hypersurfaces in Riemannian manifolds

2006-10-10

arxiv.org/abs/math/0610313v1

Mathematics

Differential Geometry

Scientific paper

Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an $m+1$-dimensional Riemannian manifold $(M^{m+1},g)$, which concentrate at a point $p_0$ (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of $p_0$. In this paper we extend this result to the other curvatures (the $r$-th mean curvature for $1\le r\le m$).

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