We study the global behavior of complete minimal δ-stable hypersurfaces in R^(n+1) by using L^2-harmonic 1-forms.We show that a complete minimal δ-stable(δ >(n-1)~2/n^2)hypersurface in R^(n+1) has only one end.W...We study the global behavior of complete minimal δ-stable hypersurfaces in R^(n+1) by using L^2-harmonic 1-forms.We show that a complete minimal δ-stable(δ >(n-1)~2/n^2)hypersurface in R^(n+1) has only one end.We also obtain two vanishing theorems of complete noncompact quaternionic manifolds satisfying the weighted Poincar′e inequality.These results are improvements of the first author's theorems on hypersurfaces and quaternionic K¨ahler manifolds.展开更多
This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are...This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).展开更多
基金The NSF(11471145,11371309)of China and Qing Lan Project
文摘We study the global behavior of complete minimal δ-stable hypersurfaces in R^(n+1) by using L^2-harmonic 1-forms.We show that a complete minimal δ-stable(δ >(n-1)~2/n^2)hypersurface in R^(n+1) has only one end.We also obtain two vanishing theorems of complete noncompact quaternionic manifolds satisfying the weighted Poincar′e inequality.These results are improvements of the first author's theorems on hypersurfaces and quaternionic K¨ahler manifolds.
基金Partially supported by National Science Foundation of China(11426195,11771377)Natural Science Foundation of Jiangsu Province(BK20191435)。
文摘This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).
