We study the global behavior of complete minimal δ-stable hypersurfaces in Rby using L~2-harmonic 1-forms.We show that a complete minimal δ-stable(δ >(n-1)~2/n~2)hypersurface in Rhas only one end.We also obtain ...We study the global behavior of complete minimal δ-stable hypersurfaces in Rby using L~2-harmonic 1-forms.We show that a complete minimal δ-stable(δ >(n-1)~2/n~2)hypersurface in Rhas 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
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 Rby using L~2-harmonic 1-forms.We show that a complete minimal δ-stable(δ >(n-1)~2/n~2)hypersurface in Rhas 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.
