The Stable Topological-hyperbolic Space Form Problem for Complete Manifolds of Finite Volume.
An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.
We prove that a three-dimensional almost Kenmotsu manifold is locally symmetric if and only if it is locally isometric to either the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4)×ℝ.
We prove a uniqueness result of weak solutions to the Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term.
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.