非紧凑流形中规定平均曲率超曲面的最小-最大构造

arXiv - MATH - Differential Geometry Pub Date : 2024-09-11 DOI:arxiv-2409.07330

Douglas Stryker

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摘要

我们为非紧凑流形中的规定平均曲率超曲面提出了一种最小-最大理论，适用于在紧凑集外不改变符号的规定函数。我们利用这一理论证明了欧几里得空间中封闭的规定平均曲率超曲面和有限体积流形中完整的有限面积恒定平均曲率超曲面的新存在性结果。

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

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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arXiv - MATH - Differential Geometry

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