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Nonlinear diffusion equations and curvature conditions in metric measure spaces /
Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X, d, m). On the geometric side, our new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one inve...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
[2019]
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1270. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X, d, m). On the geometric side, our new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, our new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD*(K, N) condition of Bacher-Sturm. |
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| Notas: | "November 2019; Volume 262; number 1270 (seventh of 7 numbers)"--Cover |
| Descripción Física: | 1 online resource (v, 121 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 119-121) |
| ISBN: | 9781470455149 1470455145 |
| ISSN: | 0065-9266 ; |