Proper harmonic maps between asymptotically hyperbolic manifolds
Kazuo Akutagawa, Yoshihiko Matsumoto
TL;DR
This paper proves an existence theorem for harmonic maps with boundary conditions at infinity between asymptotically hyperbolic manifolds, extending previous results from hyperbolic spaces.
Contribution
It generalizes Li and Tam's hyperbolic space results to asymptotically hyperbolic manifolds, establishing new existence results for harmonic maps.
Findings
Existence of harmonic maps with prescribed boundary conditions at infinity
Extension of Li and Tam's results to a broader class of manifolds
New techniques for solving the Dirichlet problem at infinity
Abstract
Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with boundary conditions at infinity between asymptotically hyperbolic manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds