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arXiv · 2310.08363

Localization of min-max minimal hypersurfaces

Douglas Stryker
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Abstract

We show that min-max minimal hypersurfaces can be localized. As a consequence, we obtain the sharp generalization to complete manifolds of the famous Almgren-Pitts min-max theorem in closed manifolds. We use this result to prove the existence of a complete embedded finite area minimal hypersurface of index at most one in every balanced complete manifold.

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Douglas Stryker. 2023-10-12. Localization of min-max minimal hypersurfaces. https://arxiv.org/abs/2310.08363

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