An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
type: Item
instance of: scholarly article
title: An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
zbMATH Open document ID: 1310.53031
author: Nicola Gigli
published in: Analysis and Geometry in Metric Spaces
publication date: 2014-12-17T00:00:00Z
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 52-02
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C70
zbMATH DE Number: 6381432
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: measure valued Laplacian
zbMATH Keywords: optimal transport
zbMATH Keywords: \(\mathsf{RCD}(0, N)\) condition
zbMATH Keywords: Busemann function
zbMATH Keywords: Bakry-Émery contraction
zbMATH Keywords: Dirichlet energy
MaRDI profile type: Publication
full work available at URL: agms-2014-0006
OpenAlex ID: W1983736020
cites work: On Complete Manifolds With Nonnegative Ricci Curvature
cites work: Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure
cites work: Q5441008
cites work: Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
cites work: Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
cites work: Nonlinear potential theory on metric spaces
cites work: Local curvature-dimension condition implies measure-contraction property
cites work: Differentiability of Lipschitz functions on metric measure spaces
cites work: Lower bounds on Ricci curvature and the almost rigidity of warped products
cites work: On the structure of spaces with Ricci curvature bounded below. I
cites work: On the structure of spaces with Ricci curvature bounded below. II
cites work: On the structure of spaces with Ricci curvature bounded below. III
cites work: The splitting theorem for manifolds of nonnegative Ricci curvature
cites work: Q5687966
cites work: On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
cites work: On the heat flow on metric measure spaces: existence, uniqueness and stability
cites work: Optimal maps in non branching spaces with Ricci curvature bounded from below
cites work: Heat Flow on Alexandrov Spaces
cites work: A PDE approach to nonlinear potential theory in metric measure spaces
cites work: The Abresch-Gromoll inequality in a non-smooth setting
cites work: Optimal maps and exponentiation on finite-dimensional spaces with Ricci curvature bounded from below
cites work: Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
cites work: Lectures on analysis on metric spaces
cites work: Nonsmooth calculus
cites work: The Variational Formulation of the Fokker--Planck Equation
cites work: Differentiable structures on metric spaces: a primer
cites work: Duality on gradient estimates and Wasserstein controls
cites work: Weak curvature conditions and functional inequalities
cites work: Ricci curvature for metric-measure spaces via optimal transport
cites work: Finsler interpolation inequalities
cites work: Heat flow on Finsler manifolds
cites work: Non-contraction of heat flow on Minkowski spaces
cites work: The Riemannian structure of Alexandrov spaces
cites work: Alexandrov meets Lott-Villani-Sturm
cites work: Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
cites work: Local Poincaré inequalities from stable curvature conditions on metric spaces
cites work: Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
cites work: Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
cites work: Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
cites work: On the geometry of metric measure spaces. I
cites work: On the geometry of metric measure spaces. II
cites work: Optimal Transport
cites work: Lipschitz algebras and derivations. II: Exterior differentiation
DOI: 10.2478/AGMS-2014-0006
description: scientific article; zbMATH DE number 6381432