The heat equation and harmonic maps of complete manifolds

DOI10.1007/BF01232256zbMath0748.58006OpenAlexW1968507425MaRDI QIDQ1814170

Luen-Fai Tam, Peter Li

Publication date: 25 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143903

zbMATH Keywords

parabolic equationharmonic maps

Mathematics Subject Classification ID

Heat equation (35K05) Harmonic maps, etc. (58E20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (78)

A mixed elliptic-parabolic boundary value problem coupling a harmonic-like map with a nonlinear spinor ⋮ Spectral convergence under bounded Ricci curvature ⋮ Complete constant Gaussian curvature surfaces in the Minkowski space and harmonic diffeomorphisms onto the hyperbolic plane ⋮ On Euler characteristic and fundamental groups of compact manifolds ⋮ A foliated metric rigidity theorem for higher rank irreducible symmetric spaces ⋮ Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces ⋮ Locally minimizing harmonic maps from noncompact manifolds ⋮ An optimal gap theorem in a complete strictly pseudoconvex CR \((2n+1)\)-manifold ⋮ Poisson equation on some complete noncompact manifolds ⋮ Harmonic maps of bounded symmetric domains ⋮ Structure theorems for complete Kähler manifolds and applications to Lefschetz type theorems ⋮ Li-Yau inequalities in geometric analysis ⋮ Pseudo-harmonic maps from complete noncompact pseudo-Hermitian manifolds to regular balls ⋮ A non-existence theorem of proper harmonic morphisms from weakly asymptotically hyperbolic manifolds ⋮ Equivariant Schrödinger map flow on two dimensional hyperbolic space ⋮ The Dirichlet problem for harmonic maps between Damek-Ricci spaces ⋮ Harmonic Teichmüller mappings ⋮ On the boundary value problem for harmonic maps of the Poincaré disc ⋮ Dirichlet problem at infinity for harmonic maps between Carnot spaces ⋮ Gradient estimates and Liouville theorems for Dirac-harmonic maps ⋮ Harmonic Maps Between Noncompact Manifolds ⋮ Harmonic quasi-isometries of pinched Hadamard surfaces are injective ⋮ A family of conformally natural extensions of homeomorphisms of the circle ⋮ Smoothing positive currents and the existence of Kähler-Einstein metrics ⋮ On subelliptic harmonic maps with potential ⋮ On the asymptotic expansions of the proper harmonic maps between balls in Bergman metrics ⋮ The stretch of a foliation and geometric superrigidity ⋮ Harmonic maps with finite total energy ⋮ Elliptic PDEs on Compact Ricci Limit Spaces and Applications ⋮ An optimal gap theorem ⋮ On a J. C. C. Nitsche's type inequality for the hyperbolic space \(\mathbf H^3\) ⋮ Matrix Li-Yau-Hamilton inequality for the CR heat equation in pseudohermitian \((2n+1)\)-manifolds ⋮ Erratum to: ``An optimal gap theorem ⋮ Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem ⋮ Harmonicity of the inverse of a harmonic diffeomorphism ⋮ Unbounded positive entire solutions of rotationally symmetric harmonic map equations ⋮ Poincaré–Lelong equation via the Hodge–Laplace heat equation ⋮ The Douady-Earle extensions are not always harmonic ⋮ Harmonic maps from a Riemannian manifold with a pole into an Hadamard manifold with negative sectional curvatures ⋮ Sharp differential estimates of Li-Yau-Hamilton type for positive (p, p) forms on Kähler manifolds ⋮ Harmonic maps and wild Teichmüller spaces ⋮ Embeddings of surfaces in 4-manifolds. I ⋮ Geometric stochastic heat equations ⋮ The heat flow of harmonic maps from noncompact manifolds ⋮ A note on curvature estimate of the Hermitian-Yang-Mills flow ⋮ A counterexample to uniqueness and regularity for harmonic maps between hyperbolic spaces ⋮ Existence and Liouville theorems for \(V\)-harmonic maps from complete manifolds ⋮ Harmonic Diffeomorphisms of the Hyperbolic Plane ⋮ Hermitian-Einstein metrics on holomorphic vector bundles over Hermitian manifolds ⋮ On the existence of hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds ⋮ Matrix Li-Yau-Hamilton estimates for the heat equation on Kähler manifolds ⋮ A new version of the main inequality and the uniqueness of harmonic maps ⋮ Dirichlet Problem at Infinity for Harmonic Maps: Rank One Symmetric Spaces ⋮ Results on a weighted Poincaré inequality of complete manifolds ⋮ On the CR Poincaré-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds ⋮ On the existence of solutions of Poisson equation and Poincaré-Lelong equation ⋮ Harmonic Diffeomorphisms Between Hadamard Manifolds ⋮ Rigidity theorem for harmonic maps with complex normal boundary conditions ⋮ On the Dirichlet problem for harmonic maps with prescribed singularities ⋮ Liouville theorems for the ancient solution of heat flows ⋮ Heat flow of harmonic maps from noncompact manifolds ⋮ The heat flow and harmonic maps between complete manifolds ⋮ Heat equation for harmonic maps of the compactification of complete manifolds ⋮ The harmonic map heat flow on conic manifolds ⋮ Forelli type theorem in harmonic map forms ⋮ Limits of harmonic maps and crowned hyperbolic surfaces ⋮ The Poisson equation on complete manifolds with positive spectrum and applications ⋮ Short-time existence for harmonic map heat flow with time-dependent metrics ⋮ Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below ⋮ The heat flows and harmonic maps from complete manifolds into regular balls ⋮ Asymptotics of finite energy monopoles on AC 3-manifolds ⋮ Minimal maps between the hyperbolic discs and generalized Gauss maps of maximal surfaces in the anti-de-Sitter 3-space ⋮ L 2 harmonic forms and finiteness of ends ⋮ Linear trace Li-Yau-Hamilton inequality for the CR Lichnerowicz-Laplacian heat equation ⋮ Harmonic maps between unbounded convex polyhedra in hyperbolic spaces ⋮ On existence of harmonic maps from a surface to the space of its normal bundle ⋮ Hermitian-Einstein metrics for vector bundles on complete Kähler manifolds ⋮ Proper harmonic maps between asymptotically hyperbolic manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
• Heat equation and compactifications of complete Riemannian manifolds
• On the parabolic kernel of the Schrödinger operator
• On the rigidity of certain discrete groups and algebraic varieties
• On the evolution of harmonic maps in higher dimensions
• Existence and partial regularity results for the heat flow for harmonic maps
• New examples of harmonic diffeomorphisms of the hyperbolic plane onto itself
• Compact group actions and the topology of manifolds with non-positive curvature
• Boundary behavior of harmonic maps on non-smooth domains and complete negatively curved manifolds
• Harmonic maps of manifolds with boundary
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• On univalent harmonic maps between surfaces
• On the heat kernel of a complete Riemannian manifold
• Sur les applications harmoniques
• Uniqueness of \(L^ 1\) solutions for the Laplace equation and the heat equation on Riemannian manifolds
• The splitting theorem for manifolds of nonnegative Ricci curvature
• Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space
• Another Report on Harmonic Maps
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Some conditions ensuring the vanishing of harmonic differential forms with applications to harmonic maps and Yang-Mills theory
• A Report on Harmonic Maps
• Harmonic Diffeomorphisms of the Hyperbolic Plane
• On Homotopic Harmonic Maps
• Harmonic Mappings of Riemannian Manifolds

This page was built for publication: The heat equation and harmonic maps of complete manifolds