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Annals of Global Analysis and Geometry, 2016
We show that a heat kernel estimate holds based on a Kato-class condition for the negative part of Ricci curvature. This is a generalization of results based on $$L^p$$Lp-bounds on the Ricci curvature. We also establish bounds on the first Betti number.
Christian Rose
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We show that a heat kernel estimate holds based on a Kato-class condition for the negative part of Ricci curvature. This is a generalization of results based on $$L^p$$Lp-bounds on the Ricci curvature. We also establish bounds on the first Betti number.
Christian Rose
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Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below
, 2021J. Cheeger, Wenshuai Jiang, A. Naber
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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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Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below
, 2018S. Yin
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