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arxiv: 1709.03672 · v1 · submitted 2017-09-12 · 🧮 math.DG · math.GT

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

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keywords boundaryconvexhypersurfacemin-maxminimalpartialcompactcurvature
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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.

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