具有光滑边界的非经典最小化曲面

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2019-06-22 DOI:10.4310/jdg/1669998183

Camillo De Lellis, G. Philippis, J. Hirsch

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引用次数: 6

摘要

我们在$\mathbb{R}^4$上构造了一个黎曼度量$g$(任意接近欧几里德度量$g$)和一个光滑的简单闭曲线$\Gamma\子集\mathbb R^4$，使得$\Gamma$张成的唯一面积最小化曲面具有无限拓扑。此外，度量几乎是Kahler，面积最小曲面被校准。

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Nonclassical minimizing surfaces with smooth boundary

We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\Gamma\subset \mathbb R^4$ such that the unique area minimizing surface spanned by $\Gamma$ has infinite topology. Furthermore the metric is almost Kahler and the area minimizing surface is calibrated.

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来源期刊

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.