Abstract: We show that a complete Riemannian manifold of dimension with $\Ric\ geq n{-}1$ and its -st eigenvalue close to is both. Abstract: We show that for n dimensional manifolds whose the Ricci curvature is greater or equal to n-1 and for k in {1,,n+1}, the k-th. We show that a complete Riemannian manifold of dimension $n$ with $\Ric\geq n{-}1$ and its $n$-st eigenvalue close to $n$ is both Gromov-Hausdorff close.

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## Transport optimal et courbure de Ricci

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### L’équation de la chaleur associée à la courbure de Ricci

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