Abstract
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.
Citation
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. https://doi.org/10.11650/tjm/180604
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