@Article{CMR-33-1,
author = {Zhu , Peng and Zhou , Jiuru},
title = {$L^2$-Harmonic 1-Forms on Complete Manifolds},
journal = {Communications in Mathematical Research },
year = {2019},
volume = {33},
number = {1},
pages = {1--7},
abstract = {<p style="text-align: justify;">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 $\bigg(\delta&gt;\dfrac{(n-1)^2}{n^2}\bigg)$ 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&#39;s theorems on hypersurfaces and quaternionic Kähler manifolds.&nbsp;</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2017.01.01},
url = {http://global-sci.org/intro/article_detail/cmr/13440.html}
}