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The maximum injectivity radius of hyperbolic orbifolds

Fanoni, Federica

In: Geometriae Dedicata, 2015, vol. 175, no. 1, p. 281-307

On the representation of the number of integral points of an elliptic curve modulo a prime number

Rassias, Michael

In: The Ramanujan Journal, 2015, vol. 36, no. 3, p. 483-499

On a class of functions that satisfies explicit formulae involving the Möbius function

Kühn, Patrick ; Robles, Nicolas ; Roy, Arindam

In: The Ramanujan Journal, 2015, vol. 38, no. 2, p. 383-422

On the Homology Length Spectrum of Surfaces

Massart, Daniel ; Parlier, Hugo

In: International Mathematics Research Notices, 2017, vol. 2017, no. 8, p. 2367-2401

Convex geodesic bicombings and hyperbolicity

Descombes, Dominic ; Lang, Urs

In: Geometriae Dedicata, 2015, vol. 177, no. 1, p. 367-384

Equivalence of the Open KdV and the Open Virasoro Equations for the Moduli Space of Riemann Surfaces with Boundary

Buryak, Alexandr

In: Letters in Mathematical Physics, 2015, vol. 105, no. 10, p. 1427-1448

Divergent Integrals, Residues of Dolbeault Forms, and Asymptotic Riemann Mappings

Felder, Giovanni ; Kazhdan, David

In: International Mathematics Research Notices, 2017, vol. 2017, no. 19, p. 5897-5918

Morrey’s 𝜖-conformality lemma in metric spaces

Fitzi, Martin ; Wenger, Stefan

In: Proceedings of the American Mathematical Society, 2020, vol. 148, no. 10, p. 4285–4298

We provide a simpler proof and slight strengthening of Morrey's famous lemma on $ \varepsilon $-conformal mappings. Our result more generally applies to Sobolev maps with values in a complete metric space, and we obtain applications to the existence of area minimizing surfaces of higher genus in metric spaces. Unlike Morrey's proof, which relies on the measurable Riemann mapping theorem, we...

Ideal polyhedral surfaces in Fuchsian manifolds

Prosanov, Roman

In: Geometriae Dedicata, 2020, vol. 206, no. 1, p. 151–179

Let Sg,n be a surface of genus g>1 with n>0 punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a...

On right-angled polygons in hyperbolic space

Dotti, Edoardo ; Drewitz, Simon T.

In: Geometriae Dedicata, 2019, vol. 200, no. 1, p. 45–59

We study oriented right-angled polygons in hyperbolic spaces of arbitrary dimensions, that is, finite sequences (S0,S1,…,Sp−1) of oriented geodesics in the hyperbolic space HHn+2 such that consecutive sides are orthogonal. It was previously shown by Delgove and Retailleau (Ann Fac Sci Toulouse Math 23(5):1049–1061, 2014. https://doi.org/10.5802/afst.1435) that three quaternionic...