具有三个边界顶点的测地线网

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2018-03-10 DOI:10.4310/jdg/1631124286

Fabian Parsch

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引用次数: 3

摘要

我们证明了在非正曲面上具有三个边界（=不平衡）顶点的测地线网至多有一个平衡顶点。我们不假设不平衡顶点的度有任何先验界。即使在欧几里得的情况下，这个结果似乎也是新的。我们通过例子证明，对于平面上正曲率的度量，这个结果是不成立的，并且对于具有四个不平衡顶点的测地线网，这个结果没有立即推广。

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Geodesic nets with three boundary vertices

We prove that a geodesic net with three boundary (= unbalanced) vertices on a non-positively curved plane has at most one balanced vertex. We do not assume any a priori bound for the degrees of unbalanced vertices. The result seems to be new even in the Euclidean case. We demonstrate by examples that the result is not true for metrics of positive curvature on the plane, and that there are no immediate generalizations of this result for geodesic nets with four unbalanced vertices.

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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.