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.
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页码：1403 / 1425
页数：23
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