Infinite energy harmonic maps from Riemann surfaces to CAT(0) spaces
Georgios Daskalopoulos, Chikako Mese
TL;DR
This paper investigates harmonic maps with potentially infinite energy from punctured Riemann surfaces to CAT(0) spaces, providing energy growth estimates near punctures and establishing their uniqueness.
Contribution
It introduces new results on the behavior and uniqueness of infinite energy harmonic maps from punctured Riemann surfaces to CAT(0) spaces.
Findings
Energy growth estimates near punctures
Uniqueness of harmonic maps with infinite energy
Characterization of harmonic maps in this setting
Abstract
We present some results about harmonic maps with possibly infinite energy from punctured Riemann surfaces to CAT(0) spaces. In particular, we give precise estimates of their energy growth near the punctures and prove their uniqueness.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology