Geodesic nets on non-compact Riemannian manifolds

被引：1

作者：

Chambers, Gregory R. ^{[1
]}

Liokumovich, Yevgeny ^{[2
]}

Nabutovsky, Alexander ^{[2
]}

Rotman, Regina ^{[2
]}

机构：

[1] Rice Univ, Dept Math, MS 136,Box 1892, Houston, TX 77251 USA

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2023年 / 2023卷 / 799期

基金：

加拿大自然科学与工程研究理事会;

关键词：

CLOSED GEODESICS;

D O I：

10.1515/crelle-2023-0028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A geodesic flower is a finite collection of geodesic loops based at the same point ?? that satisfy the following balancing condition: the sum of all unit tangent vectors to all geodesic arcs meeting at ?? is equal to the zero vector. In particular, a geodesic flower is a stationary geodesic net. We prove that, in every complete non-compact manifold with locally convex ends, there exists a non-trivial geodesic flower.

引用

页码：287 / 303

页数：17

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