A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

Copyright q 2010 Zisheng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound...

Lower Bound Estimate for the First Eigenvalue of Compact Manifolds with Negative Lower Bound of Ricci Curvature

We estimate the lower bound of the first non-zero eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang.

Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

We prove a new kind of estimate that holds on any manifold with a lower Ricci bound. It relates the geometry of two small balls with the same radius, potentially far apart, but centered in the interior of a common minimizing geodesic. It reveals new, previously unknown, properties that all generalized spaces with a lower Ricci curvature bound must have and it has a number of applications. This ...

The Ricci Flow on Radially Symmetric R

Symmetric symplectic spaces with Ricci-type curvature

We determine the isomorphism classes of symmetric symplectic manifolds of dimension at least 4 which are connected, simply-connected and have a curvature tensor which has only one non-vanishing irreducible component – the Ricci tensor.