On the exponent of convergence of negatively curved manifolds without Green's function

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2018-01-01 DOI:10.5565/PUBLMAT6211809

M. Melian, José M. Rodríguez, E. Tourís

引用次数: 0

Abstract

In this paper we prove that for every complete n-dimensional Riemannian manifold without Green’s function and with its sectional curvatures satisfying K ≤−1, the exponent of convergence is greater than or equal to n − 1. Furthermore, we show that this inequality is sharp. This result is well known for manifolds with constant sectional curvatures K = −1.

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无格林函数负弯曲流形的收敛指数

证明了对于每一个不含格林函数且截面曲率满足K≤- 1的完备n维黎曼流形，其收敛指数大于等于n- 1。此外，我们证明了这种不平等是尖锐的。这个结果对于截面曲率K = - 1为常数的流形是众所周知的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.