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arXiv · 1503.02938

Minimal hypersurfaces of least area

Laurent Mazet·Harold Rosenberg
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Abstract

In this paper, we study closed embedded minimal hypersurfaces in a Riemannian $(n+1)$-manifold ($2\le n\le 6$) that minimize area among such hypersurfaces. We show they exist and arise either by minimization techniques or by min-max methods: they have index at most $1$. We apply this to obtain a lower area bound for such minimal surfaces in some hyperbolic $3$-manifolds.

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Laurent Mazet, Harold Rosenberg. 2015-03-19. Minimal hypersurfaces of least area. https://arxiv.org/abs/1503.02938

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