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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 |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
[2019]
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1270. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Chapter 1. Introduction Chapter 2. Contraction and Convexity via Hamiltonian Estimates: an Heuristic Argument Part 1. Nonlinear Diffusion Equations and Their Linearization in Dirichlet Spaces Chapter 3. Dirichlet Forms, Homogeneous Spaces and Nonlinear Diffusion Chapter 4. Backward and Forward Linearizations of Nonlinear Diffusion Part 2. Continuity Equation and Curvature Conditions in Metric Measure Spaces Chapter 5. Preliminaries Chapter 6. Absolutely Continuous Curves in Wasserstein Spaces and Continuity Inequalities in a Metric Setting Chapter 7. Weighted Energy Functionals along Absolutely Continuous Curves Chapter 8. Dynamic Kantorovich Potentials, Continuity Equation and Dual Weighted Cheeger Energies Chapter 9. The \RCDS KN Condition and Its Characterizations through Weighted Convexity and Evolution Variational Inequalities Part 3. Bakry-¡mery Condition and Nonlinear Diffusion Chapter 10. The Bakry-¡mery Condition Chapter 11. Nonlinear Diffusion Equations and Action Estimates Chapter 12. The Equivalence Between \BE KN and \RCDS KN.