[Une condition de type courbure-dimension pour des espaces métriques mesurés]
Nous présentons une condition de type courbure-dimension
Notre condition est stable pour la convergence. Elle comporte des conséquences géométriques diverses, comme les théorèmes de Bishop–Gromov et de Bonnet–Myers. Dans les deux cas, on obtient des estimations optimales connues dans le cas riemannien.
We present a curvature-dimension condition
Our curvature-dimension condition is stable under convergence. Furthermore, it entails various geometric consequences e.g. the Bishop–Gromov theorem and the Bonnet–Myers theorem. In both cases, we obtain the sharp estimates known from the Riemannian case.
Accepté le :
Publié le :
Karl-Theodor Sturm 1
@article{CRMATH_2006__342_3_197_0, author = {Karl-Theodor Sturm}, title = {A curvature-dimension condition for metric measure spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {197--200}, publisher = {Elsevier}, volume = {342}, number = {3}, year = {2006}, doi = {10.1016/j.crma.2005.11.008}, language = {en}, }
Karl-Theodor Sturm. A curvature-dimension condition for metric measure spaces. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 197-200. doi : 10.1016/j.crma.2005.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.008/
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