Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature

Stéphane Sabourau

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arXiv · 1408.4470

Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature

Stéphane Sabourau

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Abstract

We establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse function whose level set volume is bounded in terms of the volume of the manifold. As a consequence of this sweep-out estimate, there exists an embedded, closed (possibly singular) minimal hypersurface whose volume is bounded in terms of the volume of the manifold.

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BibTeX RIS

Stéphane Sabourau. 2014-08-19. Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature. https://arxiv.org/abs/1408.4470

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