Open Access
December, 2018 The Number of Cusps of Complete Riemannian Manifolds with Finite Volume
Thac Dung Nguyen, Ngoc Khanh Nguyen, Ta Cong Son
Taiwanese J. Math. 22(6): 1403-1425 (December, 2018). DOI: 10.11650/tjm/180604


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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Thac Dung Nguyen. Ngoc Khanh Nguyen. Ta Cong Son. "The Number of Cusps of Complete Riemannian Manifolds with Finite Volume." Taiwanese J. Math. 22 (6) 1403 - 1425, December, 2018.


Received: 26 December 2017; Revised: 23 May 2018; Accepted: 11 June 2018; Published: December, 2018
First available in Project Euclid: 12 July 2018

zbMATH: 07021696
MathSciNet: MR3880236
Digital Object Identifier: 10.11650/tjm/180604

Primary: 53C23 , 53C24 , 58J50

Keywords: $p$-Laplacian , cusps , decay estimate , smooth metric measure spaces , volume comparison theorem

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 6 • December, 2018
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