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

Abstract

Let $(M^{n+1},\partial M,g)$ be a compact manifold with non-negative Ricci curvature, convex boundary and $2\le n\le 6$. 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.

27 pages

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