Bound Of Ricci Curvature Research Articles

The first Dirichlet eigenvalue of a compact manifold and the Yang conjecture

We give a new estimate on the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature and provide a solution for a conjecture of H. C. Yang. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Lower bounds of the eigenvalues of compact manifolds with positive Ricci curvature

We give new estimates on the lower bounds for the first closed and Neumann eigenvalues for compact manifolds with positive Ricci curvature in terms of the diameter and the lower bound of Ricci curvature. The results sharpen the previous estimates.

A universal bound on the gradient of logarithm of the heat kernel for manifolds with bounded Ricci curvature

We derive a gradient estimate for the logarithm of the heat kernel on a Riemannian manifold with Ricci curvature bounded from below. The bound is universal in the sense that it depends only on the lower bound of Ricci curvature, dimension and diameter of the manifold. Imposing a more restrictive non-collapsing condition allows one to sharpen this estimate for the values of time parameter close to zero.

Comparison Geometry With L1-Norms of Ricci Curvature

AbstractWe investigate the geometry of manifolds with bounded Ricci curvature in L1-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem.

Orbifold compactness for spaces of Riemannian metrics and applications

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such compactness for spaces of Bach-flat (for example half-conformally flat) metrics on 4-manifolds, and related results for metrics which are critical points of other natural Riemannian functionals on the space of metrics.

On the singularities of spaces with bounded Ricci curvature

On the singularities of spaces with bounded Ricci curvature

Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator

We establish, by simple semigroup arguments, a Levy–Gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature.

An estimate of sectional curvatures of hypersurfaces with positive Ricci curvatures

Let M be a hypersurface in Euclidean space and let the Ricci curvature of M be bounded below by some nonnegative constant. In this paper, we estimate the sectional curvature of M in terms of the lower bound of Ricci curvature and the upper bound of mean curvature.

Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds

Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds