20 citations · 169 across the 52 of their papers we have counts for
8 papers · 1 filter
Interrogating surface length spectra and quantifying isospectrality
Hugo Parlier
This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer…
On the homology length spectrum of surfaces
Daniel Massart, Hugo Parlier
On a surface with a Finsler metric, we investigate the asymptotic growth of the number of closed geodesics of length less than which minimize length among all geodesic multicur…
Short loop decompositions of surfaces and the geometry of Jacobians
Florent Balacheff, Hugo Parlier, Stéphane Sabourau
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in thr…
Constructing metrics on a -torus with a partially prescribed stable norm
Eran Makover, Hugo Parlier, Craig J. Sutton
A result of Bangert states that the stable norm associated to any Riemannian metric on the -torus is strictly convex. We demonstrate that the space of stable norms associa…
Minimal length of two intersecting simple closed geodesics
Thomas Gauglhofer, Hugo Parlier
On a hyperbolic Riemann surface, given two simple closed geodesics that intersect times, we address the question of a sharp lower bound on the length attained by the long…
A geometric characterization of orientation reversing involutions
Antonio F. Costa, Hugo Parlier
We give a geometric characterization of compact Riemann surfaces admitting orientation reversing involutions with fixed points. Such surfaces are generally called real surfaces and…
Fixed point free involutions on Riemann surfaces
Hugo Parlier
Involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface of even genus with an arbitrary Riemannian metric admitting a…
Collars and partitions of hyperbolic cone-surfaces
Emily B. Dryden, Hugo Parlier
For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove simil…