A semigroup approach to harmonic maps

DOI10.1007/s11118-004-7740-zzbMath1078.58010OpenAlexW1978963048MaRDI QIDQ1781874

Karl-Theodor Sturm

Publication date: 9 June 2005

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-004-7740-z

zbMATH Keywords

Dirichlet problemMarkov semigroupharmonic mapHadamard spacecouplingbarycenternonlinear Markov operatorWasserstein distanceNPC space

Mathematics Subject Classification ID

Probabilistic potential theory (60J45) Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20)

Related Items (15)

Approximation for convex functionals on non-positively curved spaces and the Trotter–Kato product formula ⋮ Indices of Dirichlet forms ⋮ A new proof of the Lie–Trotter–Kato formula in Hadamard spaces ⋮ Monotonicity of time-dependent transportation costs and coupling by reflection ⋮ Harmonic mappings valued in the Wasserstein space ⋮ Harmonic functions of general graph Laplacians ⋮ Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps ⋮ Lipschitz continuity of harmonic maps between Alexandrov spaces ⋮ Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above ⋮ Quantitative gradient estimates for harmonic maps into singular spaces ⋮ Expectations and martingales in metric spaces ⋮ Harmonic mappings between singular metric spaces ⋮ Discrete-time gradient flows and law of large numbers in Alexandrov spaces ⋮ Convergence of nonlinear semigroups under nonpositive curvature ⋮ The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the evolution of harmonic mappings of Riemannian surfaces
• A mapping of Riemannian manifolds which preserves harmonic functions
• Stochastic calculus in manifolds. With an appendix by P.A. Meyer
• Harmonic analysis of probability measures on hypergroups
• Introduction to the theory of (non-symmetric) Dirichlet forms
• An existence theorem for harmonic mappings of Riemannian manifolds
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• Equilibrium maps between metric spaces
• Barycenters and martingales on a manifold
• Potential theory on infinite-dimensional Abelian groups. Transl. from the Russian by Carol Regher
• Probability theory. Translated from the German by Robert B. Burckel
• Global existence theorems for harmonic maps to nonlocally compact spaces
• Sobolev spaces and harmonic maps between singular spaces
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Nonlinear Markov operators, discrete heat flow, and harmonic maps between singular spaces
• Harmonic maps into singular spaces and \(p\)-adic superrigidity for lattices in groups of rank one
• The manifold-valued Dirichlet problem for symmetric diffusions
• Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature
• Sobolev spaces and harmonic maps for metric space targets
• Brownian motion and the formation of singularities in the heat flow for harmonic maps
• Generalized Dirichlet forms and harmonic maps
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Harmonic mappings into Riemannian manifolds with non-positive sectional curvature.
• HÖLDER CONTINUITY OF THE DIRICHLET SOLUTION FOR A GENERAL DOMAIN
• The Dirichlet problem for harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature
• Harmonic Mappings of Riemannian Manifolds
• Boundary value problems and Markov processes
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• The geometry of Markov diffusion generators
• Nonlinear Markov operators associated with symmetric Markov kernels and energy minimizing maps between singular spaces
• On the absolute continuity of Gaussian measures on locally compact groups

This page was built for publication: A semigroup approach to harmonic maps