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

François Fillastre (1, 2, 3) , Andrea Seppi (4)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 CRM - Centre de Recherches Mathématiques [Montréal]
3 IRL CRM-CNRS - International Research Lab
4 IF - Institut Fourier

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

Domaines: Mathématiques [math]

François Fillastre, Andrea Seppi. A remark on one-harmonic maps from a Hadamard surface of pinched negative curvature to the hyperbolic plane. Josai Mathematical Monographs, 2021, 13, pp.63-171. ⟨10.20566/13447777_13_163⟩. ⟨hal-03246924v2⟩