Výsledky vyhledávání - "Hugo Parlier"

Autor: Nhat Minh Doan, Hugo Parlier, Ser Tan

We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we deduce two re

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dcabb9677e8465a2a0b238e8e683fec7
http://arxiv.org/abs/2002.02738

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The simple separating systole for hyperbolic surfaces of large genus

Autor: Hugo Parlier, Yunhui Wu, Yuhao Xue

In this note we show that the expected value of the separating systole of a random surface of genus $g$ with respect to Weil-Petersson volume behaves like $2\log g $ as the genus goes to infinity. This is in strong contrast to the behavior of the exp

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Counting curves, and the stable length of currents

Autor: Juan Souto, Hugo Parlier, Viveka Erlandsson

Publikováno v: Erlandsson, V, Parlier, H & Souto, J 2020, ' Counting curves, and the stable length of currents ', Journal of the European Mathematical Society, vol. 22, no. 6, pp. 1675–1702 . https://doi.org/10.4171/JEMS/953
28 pages, 6 figures. 2016
Journal of the European Mathematical Society
Journal of the European Mathematical Society, European Mathematical Society, 2020, 22 (6), pp.1675-1702. ⟨10.4171/JEMS/953⟩
Journal of the European Mathematical Society, 2020, 22 (6), pp.1675-1702. ⟨10.4171/JEMS/953⟩
ArXiv e-prints, 1612. (2016).

Let $\gamma_0$ be a curve on a surface $\Sigma$ of genus $g$ and with $r$ boundary components and let $\pi_1(\Sigma)\curvearrowright X$ be a discrete and cocompact action on some metric space. We study the asymptotic behavior of the number of curves

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http://orbilu.uni.lu/handle/10993/45393

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Short closed geodesics with self-intersections

Autor: Hugo Parlier, Viveka Erlandsson

Publikováno v: ArXiv e-prints, 1609. (2016).
Erlandsson, V & Parlier, H 2020, ' Short closed geodesics with self-intersection ', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 169, no. 3, pp. 623-638 . https://doi.org/10.1017/S030500411900032X

Our main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer $k$, we are interested in the set of all closed geodesics with at least $k$ (but possibly more) self-intersections. Among these, we consider those of

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http://orbilu.uni.lu/handle/10993/45391

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Arc and curve graphs for infinite-type surfaces

Autor: Javier Aramayona, Ariadna Fossas, Hugo Parlier

Publikováno v: Proceedings of the American Mathematical Society. 145:4995-5006

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this

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https://doi.org/10.1090/proc/13608

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Chromatic numbers of the hyperbolic surfaces

Autor: Hugo Parlier, Camille Petit

Publikováno v: Indiana Univ. Math. Journal
Indiana Univ. Math. J.

This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the $d$-chromatic number is the minimum number of colors needed to color the points of the space so that any two points at distance $d$ are of a different color. We p

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The homology systole of hyperbolic Riemann surfaces

Autor: Hugo Parlier

Publikováno v: Geom. Ded.

The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole. The same result is shown to be true for once-punctured surfaces,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81561b8e8b4d38282f84fffa2eef4378
http://doc.rero.ch/record/319467/files/10711_2011_Article_9613.pdf

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Modular flip-graphs of one-holed surfaces

Autor: Hugo Parlier, Lionel Pournin

We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus $g$ with a single boundary curve and $n$

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http://orbilu.uni.lu/handle/10993/45388

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Minimal length product over homology bases of manifolds

Autor: Steve Karam, Hugo Parlier, Florent Balacheff

Minkowski's second theorem can be stated as an inequality for $n$-dimensional flat Finsler tori relating the volume and the minimal product of the lengths of closed geodesics which form a homology basis. In this paper we show how this fundamental res

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