Complete manifolds with nonnegative Ricci curvature and almost best Sobolev constant
نویسندگان
چکیده
منابع مشابه
Conformally Flat Manifolds with Nonnegative Ricci Curvature
We show that complete conformally flat manifolds of dimension n > 3 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to R n or a spherical spaceform Sn/Γ. This extends previous results due to Q.-M. Cheng and B.-L. Chen and X.-P. Zhu. In this note, we study compl...
متن کاملComplete Manifolds of Nonnegative Curvature
The purpose of this survey is to give an overview of the results which characterize Riemannian manifolds with nonnegative or positive sectional, Ricci and scalar curvature, putting an emphasis on the differences between these increasingly strong conditions on curvature. All manifolds considered here are assumed to be complete. First we consider how nonnegative curvature is different from positi...
متن کاملRigidity of Compact Manifolds with Boundary and Nonnegative Ricci Curvature
Let Ω be an (n + 1)-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary M = ∂Ω. Assume that the principal curvatures of M are bounded from below by a positive constant c. In this paper, we prove that the first nonzero eigenvalue λ1 of the Laplacian of M acting on functions on M satisfies λ1 ≥ nc2 with equality holding if and only if Ω is isometric to a...
متن کاملComplete Manifolds with Nonnegative Curvature Operator
In this short note, as a simple application of the strong result proved recently by Böhm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension ≥ 3) whose curvature operator is bounded and satisfies the pinching condition ...
متن کاملOn the Fundamental Group of Manifolds with Almost Nonnegative Ricci Curvature
Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2001
ISSN: 0019-2082
DOI: 10.1215/ijm/1258138064