Year: 2017
Author: Peng Zhu, Jiuru Zhou
Communications in Mathematical Research , Vol. 33 (2017), Iss. 1 : pp. 1–7
Abstract
We study the global behavior of complete minimal $\delta$-stable hypersurfaces in $\mathbf{R}^{n+1}$ by using $L^2$-harmonic 1-forms. We show that a complete minimal $\delta$-stable $\bigg(\delta>\dfrac{(n-1)^2}{n^2}\bigg)$ hypersurface in $\mathbf{R}^{n+1}$ has only one end. We also obtain two vanishing theorems of complete noncompact quaternionic manifolds satisfying the weighted Poincaré inequality. These results are improvements of the first author's theorems on hypersurfaces and quaternionic Kähler manifolds.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2017.01.01
Communications in Mathematical Research , Vol. 33 (2017), Iss. 1 : pp. 1–7
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 7
Keywords: minimal hypersurface end quaternionic manifold weighted Poincaré inequality