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arXiv · 1704.00130

The number of cusps of complete Riemannian manifolds with finite volume

Nguyen Thac Dung·Nguyen Ngoc Khanh·Ta Cong Son
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Abstract

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.

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Nguyen Thac Dung, Nguyen Ngoc Khanh, Ta Cong Son. 2017-04-01. The number of cusps of complete Riemannian manifolds with finite volume. https://arxiv.org/abs/1704.00130

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