In: Geometriae Dedicata, 2015, vol. 175, no. 1, p. 281-307
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In: Mathematische Zeitschrift, 2009, vol. 262, no. 3, p. 603-611
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In: Geometriae Dedicata, 2012, vol. 157, no. 1, p. 331-338
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In: Geometriae Dedicata, 2005, vol. 115, no. 1, p. 121-133
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In: Geometric and Functional Analysis, 2011, vol. 21, no. 5, p. 1069-1090
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In: Geometriae Dedicata, 2015, vol. 175, no. 1, p. 281–307
For two-dimensional orientable hyperbolic orbifolds, we show that the radius of a maximal embedded disk is greater or equal to an explicit constant ρT, with equality if and only if the orbifold is a sphere with three cone points of order 2, 3 and 7.
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In: Geometric and functional analysis, 2012, vol. 22, no. 1, p. 37-73
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 three different directions.First, we find bounds on the lengths of homologically independent curves on closed Riemannian surfaces. As a consequence, we show that for any l Î (0, 1) there exists a constant C λ such that...
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In: Geometriae Dedicata, 2012, vol. 157, no. 1, p. 331-338
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, and is shown to fail for surfaces with a large number of cusps.
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In: Geometric and Functional Analysis, 2011, vol. 21, no. 5, p. 1069-1090
Our goal is to show, in two different contexts, that “random” surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus g for which any pants decomposition requires curves of total length at least g7/6−ε. Moreover, we prove that this bound holds for most metrics in the modulispace of hyperbolic metrics equipped with the Weil–Petersson volume...
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In: Bulletin des Sciences Mathématiques, 2004, vol. 128, p. 739-748
In this article we give two new infinite sequences of perfect non-extremal Riemann surfaces of genus bigger than six. The first sequence consists of weakly eutactic perfect surfaces; the second one of semi-eutactic perfect surfaces.
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