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Some of the next articles are maybe not open access.
1998
In this chapter we shall introduce some of the fundamental theorems for manifolds with lower Ricci curvature bounds. Two important techniques will be developed: relative volume comparison and weak upper bounds for the Laplacian of distance functions.
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In this chapter we shall introduce some of the fundamental theorems for manifolds with lower Ricci curvature bounds. Two important techniques will be developed: relative volume comparison and weak upper bounds for the Laplacian of distance functions.
openaire +1 more source
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 $$ {R_{{ij}}} = \frac{1}{{2(n - 1)}}{g^{{k2}}}\left[ {\frac{{{\partial ^{2}}}}{{\partial {x^{1}}\partial {x^{k}}}}{g_{{j2}}} + \frac{{{\partial ^{2}}}}{{\partial {x^{j}}\partial {x^{2}}}}{g_{{ik}}} - \frac{{{\partial ^{2}}}
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Let g = {gij be a Riemannian metric on a manifold M of dimension n. It is Ricci curvature Rc(g) = {Rij} is given by the formula $$ {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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Holographic dark energy model from Ricci scalar curvature
Physical Review D, 2009Changjun Gao, Xuelei Chen
exaly
Bakry–Émery curvature-dimension condition and Riemannian Ricci curvature bounds
Annals of Probability, 2015Luigi Ambrosio, Nicola Gigli
exaly
Asymptotic safety of quantum gravity beyond Ricci scalars
Physical Review D, 2018Kevin Falls +2 more
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Mapping Ricci-based theories of gravity into general relativity
Physical Review D, 2018Gonzalo J Olmo, Diego Rubiera-Garcia
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