Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments
From MaRDI portal
Publication:6064557
DOI10.4171/8ecm/35MaRDI QIDQ6064557
Publication date: 10 November 2023
Published in: European Congress of Mathematics (Search for Journal in Brave)
Ricci curvaturemetric measure spaceoptimal transportcurvature-dimension conditionBakry-Émerysynthetic Ricci bound
Dirichlet forms (31C25) Heat equation (35K05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Schrödinger and Feynman-Kac semigroups (47D08) Analysis on metric spaces (30L99)
Cites Work
- Ricci flow, entropy and optimal transportation
- Gradient flows on Wasserstein spaces over compact Alexandrov spaces
- Polar factorization and monotone rearrangement of vector‐valued functions
- The Variational Formulation of the Fokker--Planck Equation
- Non-collapsed spaces with Ricci curvature bounded from below
- Heat Flow on Time‐Dependent Metric Measure Spaces and Super‐Ricci Flows
- On the volume measure of non-smooth spaces with Ricci curvature bounded below
- Heat Flow on Alexandrov Spaces
- On a conjecture of Cheeger
- Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
- Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
- Scaling Limits of Discrete Optimal Transport
- Rigidity for the spectral gap on Rcd(K, ∞)-spaces
- Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
- Dissipative Quantum Mechanics Using GENERIC
- Book Review: Geometry of isotropic convex bodies
- Functional inequalities for the heat flow on time‐dependent metric measure spaces
- Polar factorization of maps on Riemannian manifolds
- Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces
- Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models
- Ricci curvature in dimension 2
- An optimal transport formulation of the Einstein equations of general relativity
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
- Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
- Gradient flows of the entropy for jump processes
- An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy
- Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
- Displacement convexity of entropy and related inequalities on graphs
- Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
- An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
- Curvature bounds for configuration spaces
- On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
- Dimension-free Harnack inequalities on \(\mathrm{RCD}(K, \infty )\) spaces
- Displacement convexity of generalized relative entropies
- Gromov-Wasserstein distances and the metric approach to object matching
- Gradient flows of the entropy for finite Markov chains
- Heat flow with Dirichlet boundary conditions via optimal transport and gluing of metric measure spaces
- Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees)
- Wasserstein space over the Wiener space
- Weak curvature conditions and functional inequalities
- Obata's rigidity theorem for metric measure spaces
- The sharp Sobolev inequality on metric measure spaces with lower Ricci curvature bounds
- Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow
- On Borell-Brascamp-Lieb inequalities on metric measure spaces
- The heat equation on manifolds as a gradient flow in the Wasserstein space
- Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
- Second fundamental form and gradient of Neumann semigroups
- On the structure of spaces with Ricci curvature bounded below. I
- Multiplicative functional for the heat equation on manifolds with boundary.
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- Some new results on eigenvectors via dimension, diameter, and Ricci curvature
- A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
- On the structure of spaces with Ricci curvature bounded below. III
- Girsanov and Feynman-Kac type transformations for symmetric Markov processes
- Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes
- Second order differentiation formula on \(\mathsf{RCD}(K,N)\) spaces
- Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces
- Singular Ricci flows. I
- Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spaces
- Neumann heat flow and gradient flow for the entropy on non-convex domains
- Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
- Li-Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class
- Bakry-Émery curvature and diameter bounds on graphs
- Ricci curvature of finite Markov chains via convexity of the entropy
- Convex functionals of probability measures and nonlinear diffusions on manifolds
- Functional inequalities on manifolds with non-convex boundary
- Super-Ricci flows for metric measure spaces
- An elementary proof of the polar factorization of vector-valued functions
- Existence and uniqueness of monotone measure-preserving maps
- Yau's gradient estimates on Alexandrov spaces
- Lower bounds on Ricci curvature and quantitative behavior of singular sets
- Second order differentiation formula on \(\mathsf{RCD}^*(K,N)\) spaces
- Korevaar-Schoen's directional energy and Ambrosio's regular Lagrangian flows
- Remarks about synthetic upper Ricci bounds for metric measure spaces
- Behaviour of the reference measure on \(\mathsf{RCD}\) spaces under charts
- Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature
- Curvature-dimension conditions under time change
- Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds
- A dual formula for the noncommutative transport distance
- Boundary regularity and stability for spaces with Ricci bounded below
- Uniqueness and stability of Ricci flow through singularities
- Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel
- Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph
- Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
- Super Ricci flows for weighted graphs
- Molecules as metric measure spaces with Kato-bounded Ricci curvature
- Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity
- New differential operator and noncollapsed RCD spaces
- Geometric inequalities for manifolds with Ricci curvature in the Kato class
- Distribution-valued Ricci bounds for metric measure spaces, singular time changes, and gradient estimates for Neumann heat flows
- Monotonicity and rigidity of the \(\mathcal{W}\)-entropy on \(\mathsf{RCD} (0, N)\) spaces
- The globalization theorem for the curvature-dimension condition
- Differential of metric valued Sobolev maps
- Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
- A sufficient condition to a regular set being of positive measure on spaces
- Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces
- Cones over metric measure spaces and the maximal diameter theorem
- Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
- Ricci curvature for metric-measure spaces via optimal transport
- Curvature and transport inequalities for Markov chains in discrete spaces
- On the geometry of metric measure spaces with variable curvature bounds
- Structure theory of metric measure spaces with lower Ricci curvature bounds
- 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
- On the geometry of metric measure spaces. I
- On the geometry of metric measure spaces. II
- Diffusion by optimal transport in Heisenberg groups
- \((K,N)\)-convexity and the curvature-dimension condition for negative \(N\)
- Li-Yau and Harnack type inequalities in \(\text{RCD}^\ast (K,N)\) metric measure spaces
- Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds
- Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds
- Metric-measure boundary and geodesic flow on Alexandrov spaces
- Rigidity of cones with bounded Ricci curvature
- Sharp Cheeger-buser type inequalities in \(\mathsf{RCD}(K,\infty)\) spaces
- Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- Gromov--Hausdorff Convergence of Discrete Transportation Metrics
- On the differential structure of metric measure spaces and applications
- Beyond traditional Curvature-Dimension I: New model spaces for isoperimetric and concentration inequalities in negative dimension
- A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
- Transport inequalities, gradient estimates, entropy and Ricci curvature
- Heat flow on Finsler manifolds
This page was built for publication: Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments