Min-max minimal hypersurface in manifolds with convex boundary and $Ric\geq 0$

Zhichao Wang

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Min-max minimal hypersurface in manifolds with convex boundary and Ricgeq 0

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arxiv 1709.03672 v1 pith:MZPA732G submitted 2017-09-12 math.DG math.GT

Min-max minimal hypersurface in manifolds with convex boundary and $Ric\geq 0$

Zhichao Wang This is my paper

classification math.DG math.GT

keywords boundaryconvexhypersurfacemin-maxminimalpartialcompactcurvature

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abstract

Let $(M^{n+1},\partial M,g)$ be a compact manifold with non-negative Ricci curvature, convex boundary and $2\leq n\leq 6$. We show that the min-max minimal hypersurface with respect to one-parameter families of hypersurfaces in $(M,\partial M)$ is orientable, of index one and multiplicity one.

Min-max minimal hypersurface in manifolds with convex boundary and $Ric\geq 0$

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