Heat and entropy flows in Carnot groups
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Publication:2177519
DOI10.4171/rmi/1129zbMath1439.53032arXiv1801.01300OpenAlexW2981956254MaRDI QIDQ2177519
Giorgio Stefani, Luigi Ambrosio
Publication date: 6 May 2020
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.01300
Heat equation (35K05) Spaces of measures, convergence of measures (28A33) Sub-Riemannian geometry (53C17)
Related Items
Lipschitz Carnot-Carathéodory structures and their limits, Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries, Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups
Cites Work
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- Gradient flow structures for discrete porous medium equations
- An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy
- Equivalent semigroup properties for the curvature-dimension condition
- Gradient flows of the entropy for finite Markov chains
- Wasserstein space over the Wiener space
- An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
- Asymptotic estimates for the heat kernel on Heisenberg groups
- Reverse Poincaré inequalities, isoperimetry, and Riesz transforms in Carnot groups
- The heat equation on manifolds as a gradient flow in the Wasserstein space
- Curvatures of left invariant metrics on Lie groups
- On the structure of finite perimeter sets in step 2 Carnot groups
- A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries
- The continuity equation on metric measure spaces
- Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
- Metric measure spaces with Riemannian Ricci curvature bounded from below
- Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
- Diffusion by optimal transport in Heisenberg groups
- Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds
- A nonholonomic Moser theorem and optimal transport
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- Alexandrov meets Lott--Villani--Sturm
- Transport inequalities, gradient estimates, entropy and Ricci curvature
- First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces
- Heat flow on Finsler manifolds
- Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group
- Stratified Lie Groups and Potential Theory for their Sub-Laplacians
- Gradient flows on Wasserstein spaces over compact Alexandrov spaces
- The Variational Formulation of the Fokker--Planck Equation
- Heat Flow on Alexandrov Spaces
- Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure
- Young measure, superposition and transport
- Optimal Transport
- On the heat flow on metric measure spaces: existence, uniqueness and stability
