On Harmonic Maps from the Complex Plane to Hyperbolic 3-Space

Article Type

Research Article

Publication Title

Journal of Geometric Analysis

Abstract

For any twisted ideal polygon in H3, we construct a harmonic map from C to H3 with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane. Our proof uses the harmonic map heat flow. We also show that such a harmonic map is unique once we prescribe the principal part of its Hopf differential.

DOI

10.1007/s12220-025-01928-2

Publication Date

3-1-2025

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