Results 251 to 260 of about 409,873 (273)

Ricci Curvature and Volume Convergence

The Annals of Mathematics, 1997
The author gives a new integral estimate of distances and angles on manifolds with a given lower Ricci curvature bound. He obtains this estimate via a Hessian estimate and states it in three different forms. Using this, he proves (among other things) the following conjectures: 1.
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Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below

, 2021
J. Cheeger, Wenshuai Jiang, A. Naber
semanticscholar   +1 more source

Small excess and Ricci curvature

Journal of Geometric Analysis, 1991
The excess of a metric space \((M,d)\) is defined to be \[ \hbox{exc}(M)=\inf_{p,q\in M}\sup_{x\in M}(d(p,x)+d(x,q)-d(p,q)). \] A closed Riemannian manifold \(M\) with vanishing excess is a twisted sphere. The author uses a compactness result of Anderson and Cheeger to show that manifolds with bounded geometry and sufficiently small excess are in fact ...
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Metrics of Negative Ricci Curvature

The Annals of Mathematics, 1994
Using some deformation techniques the author is able to construct Riemannian metrics \(g\) of negative Ricci curvature \(r(g)\) and to prove in this way the following remarkable results: (i) For any \(n \geq 3\) there exist constants \(a(n) > b(n) > 0\) such that any manifold \(M\) with \(\dim M \geq 3\) admits a complete Riemannian metric \(g\) for ...
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On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*

, 1978
S. Yau
semanticscholar   +1 more source

The Ricci Curvature Equation

1984
Let g = {gij be a Riemannian metric on a manifold M of dimension n. It is Ricci curvature Rc(g) = {Rij} is given by the formula $$ {R_{{ij}}} = \frac{1}{{2(n - 1)}}{g^{{k2}}}\left[ {\frac{{{\partial ^{2}}}}{{\partial {x^{1}}\partial {x^{k}}}}{g_{{j2}}} + \frac{{{\partial ^{2}}}}{{\partial {x^{j}}\partial {x^{2}}}}{g_{{ik}}} - \frac{{{\partial ^{2}}}
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Forman persistent Ricci curvature (FPRC)-based machine learning models for protein–ligand binding affinity prediction

Briefings in Bioinformatics, 2021
JunJie Wee, Kelin Xia
exaly  

Holographic dark energy model from Ricci scalar curvature

Physical Review D, 2009
Changjun Gao, Xuelei Chen
exaly  

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

Inventiones Mathematicae, 2013
Luigi Ambrosio, Nicola Gigli
exaly  

Bakry–Émery curvature-dimension condition and Riemannian Ricci curvature bounds

Annals of Probability, 2015
Luigi Ambrosio, Nicola Gigli
exaly