Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
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DOI：
10.1007/s00222-013-0452-5
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发表时间：
2013-12-01
影响因子：
3.1
通讯作者：
Metzger, Jan
中科院分区：
文献类型：
--
作者：
Eichmair, Michael;Metzger, Jan
等周问题给定面积所能包围的最大体积是多少？可以追溯到古代。[1]第一个数学上严格的结果是在世纪。等周问题及其密切相关的极小曲面分析是几何变分法的两个模型问题。能明确回答等周问题的几何列表很短。我们在附录H中提供了可用结果的概述。在本文和[22]中，我们用一类黎曼流形（M，g）来扩展这个列表，我们完全描述了所有大的等周区域。
The question of isoperimetry What is the largest amount of volume that can be enclosed by a given amount of area? can be traced back to antiquity. 1 The first mathematically rigorous results are as recent as the nineteenth century. The question of isoperimetry and its close relative, the analysis of minimal surfaces, are two of the model problems of the geometric calculus of variations.The list of geometries where an explicit answer to the question of isoperimetry is available is short. We provide an overview of available results in Appendix H. In this paper and [22], we extend this list by a class of Riemannian manifolds (M, g) for which we describe all large isoperimetric regions completely.