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1.
12 p, 490.1 KB Sur la systole de la sphère au voisinage de la métrique standard / Balacheff, Florent Nicolas (Université de Genève. Section de Mathématiques)
We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth Riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, admits the standard metric g 0 as a critical point, although it does not achieve the conjectured global minimum: we show that for each tangent direction to the space of metrics at g 0, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase.
2006 - 10.1007/s10711-006-9087-7
Geometriae Dedicata, Vol. 121, Issue 1 (August 2006) , p. 61-71  
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2.
Actions on products of CAT(-1)-spaces / García, Teresa (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Porti, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We show that for X a proper CAT(−1) space there is a maximal open subset of the horofunction compactification of X × X, with respect to the maximum metric, that compactifies the diagonal action of an infinite quasi-convex group of the isometries of X. [...]
2023 - 10.1007/s10711-023-00805-y
Geometriae Dedicata, Vol. 217 (June 2023) , art. 69  
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3.
15 p, 317.5 KB Connected components of Isom(H3)-representations of non-orientable surfaces / Durán Batalla, Juan Luis (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let N denote the closed non-orientable surface of genus k. In this paper we study the behaviour of the 'square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. [...]
2022 - 10.1007/s10711-022-00682-x
Geometriae Dedicata, Vol. 216, Issue 3 (June 2022) , art. 25  
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4.
17 p, 722.0 KB On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared: Quadratic polynomial differential systems have at most one algebraic limit cycle. [...]
2017 - 10.1007/s10711-017-0244-y
Geometriae Dedicata, Vol. 191 (2017) , p. 37-52  
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5.
31 p, 536.4 KB Volume entropy for minimal presentations of surface groups in all ranks / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Juher, David (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ; Los, Jérôme (Aix-Marseille Université. Institut Mathematiques de Marseille) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called minimal geomètric presentations. We rediscover a formula first obtained by Cannon and Wagreich [6] with the computation in a non published manuscrit by Cannon [5]. [...]
2015 - 10.1007/s10711-015-0103-7
Geometriae Dedicata, Vol. 180 (August 2015) , p. 293-322  
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