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arXiv · 2409.07330

Min-max construction of prescribed mean curvature hypersurfaces in noncompact manifolds

Douglas Stryker
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Abstract

We develop a min-max theory for hypersurfaces of prescribed mean curvature in noncompact manifolds, applicable to prescription functions that do not change sign outside a compact set. We use this theory to prove new existence results for closed prescribed mean curvature hypersurfaces in Euclidean space and complete finite area constant mean curvature hypersurfaces in finite volume manifolds.

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Douglas Stryker. 2024-09-11. Min-max construction of prescribed mean curvature hypersurfaces in noncompact manifolds. https://arxiv.org/abs/2409.07330

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