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arXiv · 2106.01187

A remark on one-harmonic maps from a Hadamard surface of pinched negative curvature to the hyperbolic plane

François Fillastre·Andrea Seppi
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Abstract

We show that every one-harmonic map, in the sense of Trapani and Valli, from a Hadamard surface of pinched negative curvature to $\mathbb{H}^2$ has image the interior of the convex hull of a subset of $\partial_\infty\mathbb{H}^2$. The proof relies on Minkowski geometry, by interpreting one-harmonic maps as the Gauss maps of convex surfaces.

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François Fillastre, Andrea Seppi. 2021-06-02. A remark on one-harmonic maps from a Hadamard surface of pinched negative curvature to the hyperbolic plane. https://arxiv.org/abs/2106.01187

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