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On harmonic maps from the complex plane to hyperbolic 3-space | Synapse

April 9, 2024Open Access

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On harmonic maps from the complex plane to hyperbolic 3-space

SGSubhojoy GuptaIndian Institute of Science Bangalore GSGobinda SauIndian Statistical Institute

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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.

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Gupta et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6febab6db643587678f4c https://doi.org/https://doi.org/10.48550/arxiv.2404.06354

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