We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality,then it is definite.We also discuss some new insights for compact Riemannian 4-manifolds...We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality,then it is definite.We also discuss some new insights for compact Riemannian 4-manifolds with positive sectional curvature.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
It is considered the class of Riemann surfaces with dimT1=0, where T1 is a subclass of exactharmonic forms which is one of the factors in the orthogonal decomposition of the space Ω^H of harmonic forms of the surface...It is considered the class of Riemann surfaces with dimT1=0, where T1 is a subclass of exactharmonic forms which is one of the factors in the orthogonal decomposition of the space Ω^H of harmonic forms of the surface, namely Ω^H=＊Ω^H＋T1＋＊T0^H＋T0^H＋T2The surfaces in the class OHD and the clase of planar surfaces satisfy dimT1 =0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimTl = 0 among the surfaces of the form Sg／K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.展开更多
We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then ...We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.展开更多
文摘We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a strengthened Kato type inequality,then it is definite.We also discuss some new insights for compact Riemannian 4-manifolds with positive sectional curvature.
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).
基金A.Fernández is partially supported by the Grant BFM2002-04801J.Pérez by the Grant BFM2002-00141.
文摘It is considered the class of Riemann surfaces with dimT1=0, where T1 is a subclass of exactharmonic forms which is one of the factors in the orthogonal decomposition of the space Ω^H of harmonic forms of the surface, namely Ω^H=＊Ω^H＋T1＋＊T0^H＋T0^H＋T2The surfaces in the class OHD and the clase of planar surfaces satisfy dimT1 =0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimTl = 0 among the surfaces of the form Sg／K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.
文摘We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.
