Harmonic Maps of Manifolds with Boundary

  title={Harmonic Maps of Manifolds with Boundary},
  author={Richard S. Hamilton},
Harmonic maps.- Function spaces.- Semi-elliptic and parabolic equations.- The heat equation for manifolds.- Growth estimates and convergence. 
Harmonic extensions of quasisymmetric maps
We study the Dirichlet problem for harmonic maps between hyperbolic planes, under the assumption that the Euclidean harmonic extension of the boundary map is quasiconformal.
Proper harmonic maps between asymptotically hyperbolic manifolds
Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with $$C^1$$C1 boundary conditions at infinity between
Existence of Harmonic Maps with Two-Form and Scalar Potentials
In this paper, we obtain existence results of Dirichlet problem for harmonic maps with two-form and scalar potentials from Riemannian surfaces M with nonempty boundary into compact manifolds N with
A boundary value problem for Hermitian harmonic maps and applications
We study the existence and uniqueness problems for Hermitian harmonic maps from Hermitian manifolds with boundary to Riemannian manifolds of nonpositive sectional curvature and with convex boundary.
Asymptotic Dirichlet Problem for Harmonic Maps with Bounded Image
Existence and uniqueness is proved for asymptotic Dirichlet problems on Hadamard manifolds. This includes manifolds of bounded negative curvature and symmetric spaces of higher rank.
The heat flows and harmonic maps from complete manifolds into regular balls
We generalise the existence result for harmonic maps obtained by Hildebrandt-Kaul-Widman to the case where the domain manifold is complete noncompact.
Existence and regularity results for the gradient flow for p-harmonic maps
We establish existence and regularity for a solution of the evolution problem associated to p-harmonic maps if the target manifold has a nonpositive sectional curvature.
Harmonic mappings with partially free boundary
The existence and regularity result of Hildebrandt — Kaul-Widman, concerning the Dirichlet problem for harmonic mappings between Riemannian manifolds, is extended to a mixed boundary value problem.
Blow-Up Analysis for Heat Flow of Harmonic Maps
It is investigated that in higher dimensions the heat flow of harmonic maps between two compact Riemannian manifolds blows up in a finite time if the initial map is in some nontrivial homotopic class