The Number of Cusps of Complete Riemannian Manifolds with Finite Volume

被引：1

作者：

Thac Dung Nguyen ^{[1
,2
]}

Ngoc Khanh Nguyen ^{[1
]}

Ta Cong Son ^{[1
]}

机构：

[1] Hanoi Univ Sci, Dept Math Mech & Informat, Hanoi, Vietnam

[2] Thang Long Univ, Thang Long Inst Math & Appl Sci TIMAS, Hoang Mai, HaNoi, Vietnam

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2018年 / 22卷 / 06期

关键词：

cusps; decay estimate; p-Laplacian; smooth metric measure spaces; volume comparison theorem; P-LAPLACIAN; SPECTRUM; EIGENVALUE;

D O I：

10.11650/tjm/180604

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we count the number of cusps of complete Riemannian manifolds M with finite volume. When M is a complete smooth metric measure spaces, we show that the number of cusps in bounded by the volume V of M if some geometric conditions hold true. Moreover, we use the nonlinear theory of the p-Laplacian to give a upper bound of the number of cusps on complete Riemannian manifolds. The main ingredients in our proof are a decay estimate of volume of cusps and volume comparison theorems.

引用

页码：1403 / 1425

页数：23

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