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.

arXiv comment27 pages

References in corpus (1)

• Min-max theory for free boundary minimal hypersurfaces I - regularity theory

Cited by in corpus (2)

• Free boundary minimal surfaces in the unit ball : recent advances and open questions
• Free boundary minimal hypersurfaces with least area