The number of cusps of complete Riemannian manifolds with finite volume

Autor:	Dung, Nguyen Thac, Khanh, Nguyen Ngoc, Son, Ta Cong
Rok vydání:	2017
Předmět:	Mathematics - Differential Geometry Primary 53C23 Secondary 53C24 58J0
Druh dokumentu:	Working Paper
Popis:	In this paper, we will 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. Comment: Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1704.00130 Zobrazit plný text záznamu View this record from Arxiv