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
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
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
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.
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).
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.
