Porous media equation and Sobolev inequalities under negative curvature |
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Authors: | Jérôme Demange |
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Institution: | Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France |
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Abstract: | We study the link between some modified porous media equation and Sobolev inequalities on a Riemannian manifold M whose Ricci curvature tensor is bounded below by a negative constant −ρ. The method used deals with entropy-energy differentiation and follows the way the author got inequalities under nonnegative Ricci curvature assumptions. The key of the proof is the curvature-dimension criterion. |
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Keywords: | Porous media equation Sobolev inequalities Curvature-dimension criterion |
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