In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising simila...In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrodinger operators under geometric flows.We also pose three questions which we consider to be of a general interest.展开更多
基金supported in part by Young Faculty Career Start Program (34000-3171917)NSFC (10901165)+1 种基金NSFGD (9451027501002600)China Postdoc-toral Science Foundation (20090460066)
文摘In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.
文摘In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrodinger operators under geometric flows.We also pose three questions which we consider to be of a general interest.
