Metric structure of cut loci in surfaces and Ambrose's problem
Metric structure of cut loci in surfaces and Ambrose's problem
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表面切割轨迹的度量结构和安布罗斯问题
DOI：
10.4310/jdg/1214455780
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发表时间：
1994
影响因子：
2.5
通讯作者：
J. Hebda
中科院分区：
文献类型：
--
作者：
J. Hebda
结果表明，完整的二维黎曼流形中一点的割轨迹的每个紧子集都具有有限的一维豪斯多夫测度。当与早期论文的结果相结合时，这就完成了安布罗斯长期存在的问题的二维情况的解决方案。
It is shown that every compact subset of the cut locus of a point in a com- plete, two-dimensional Riemannian manifold has finite one-dimensional Hausdorff measure. When combined with a result from an earlier paper, this completes the solution of the two-dimensional case of a long-standing problem of Ambrose.