We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spe...We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.展开更多
In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.
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Supported by the National Key R and D Program of China(2020YFA0713100)the Natural Science Foundation of Jiangsu Province(BK20230900)National Natural Science Foundation of China(12141104)。
文摘We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.
基金The NSF(11101352) of ChinaNew Century Talent Project of Yangzhou University,Fund of Jiangsu University of Technology(KYY 13005)Qing Lan Project
文摘In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.
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.
