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It is well known that M admits a unique foliation by constant mean ... [more ▼]Let M be a globally hyperbolic maximal compact 3-dimensional spacetime locally modelled on Minkowski, anti-de Sitter or de Sitter space. It is well known that M admits a unique foliation by constant mean curvature surfaces. In this paper we extend this result to singular spacetimes with particles (cone singularities of angles less than π along time-like geodesics). [less ▲]Detailed reference viewed: 68 (4 UL) Character varieties for real formsAcosta, Miguel in Geometriae Dedicata (2019)Let $\Gamma$ be a finitely generated group and G a real form of SL(n,C). We propose a definition for the G-character variety of $\Gamma$ as a subset of the SL(n,C)-character variety of $\Gamma$. We ... [more ▼]Let $\Gamma$ be a finitely generated group and G a real form of SL(n,C). We propose a definition for the G-character variety of $\Gamma$ as a subset of the SL(n,C)-character variety of $\Gamma$. We consider two anti-holomorphic involutions of the SL(n,C)-character variety and show that an irreducible representation with character fixed by one of them is conjugate to a representation taking values in a real form of SL(n,C). We study in detail an example: the SL(n,C), SU(2,1) and SU(3) character varieties of the free product Z/3Z*Z/3Z. [less ▲]Detailed reference viewed: 59 (1 UL) Bad irreducible subgroups and singular locus for character varieties in PSL(p,C)Guerin, Clément in Geometriae Dedicata (2017)We give the centralizers of irreducible representations from a finitely generated group $\Gamma$ to $PSL(p,\mathbb{C})$ where p is a prime number. This leads to a description of the singular locus (te ... [more ▼]We give the centralizers of irreducible representations from a finitely generated group $\Gamma$ to $PSL(p,\mathbb{C})$ where p is a prime number. This leads to a description of the singular locus (te (the set of conjugacy classes of representations whose centralizer strictly contains the center of the ambient group) of the irreducible part of the character variety $\chi^i(\Gamma,PSL(p,\mathbb{C}))$. When $\Gamma$ is a free group of rank $l\geq 2$ or the fundamental group of a closed Riemann surface of genus $g\geq 2$, we give a complete description of this locus and prove that this locus is exactly the set of algebraic singularities of the irreducible part of the character variety. [less ▲]Detailed reference viewed: 194 (5 UL) Conformal essential actions of PSL(2,R) on real-analytic compact Lorentz manifoldsPecastaing, Vincent in Geometriae Dedicata (2017), 188(1), 171-194The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least three admitting a conformal essential action of a Lie group locally isomorphic to ... [more ▼]The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least three admitting a conformal essential action of a Lie group locally isomorphic to PSL(2,R). It is established by using a general result on local isometries of real-analytic rigid geometric structures. As corollary, we deduce the same conclusion for conformal essential actions of connected semi-simple Lie groups on real-analytic compact Lorentz manifolds. This work is a contribution to the understanding of the Lorentzian version of a question asked by A. Lichnerowicz. [less ▲]Detailed reference viewed: 46 (3 UL) On an extension of the H^k mean curvature flow of closed convex hypersurfacesLi, Yi in Geometriae Dedicata (2014), 172(1), 147-154Detailed reference viewed: 46 (2 UL) Harnack estimates for geometric flows, applications to Ricci flow coupled with harmonic map flowGuo, Hongxin ; He, Tongtongin Geometriae Dedicata (2014), 169(1), 411-418We derive Harnack estimates for heat and conjugate heat equations in abstract geometric flows. The main results lead to new Harnack inequalities for a variety of geometric flows. In particular, Harnack ... [more ▼]We derive Harnack estimates for heat and conjugate heat equations in abstract geometric flows. The main results lead to new Harnack inequalities for a variety of geometric flows. In particular, Harnack inequalities for the Ricci flow coupled with Harmonic map flow are obtained. [less ▲]Detailed reference viewed: 128 (2 UL) Notes on: Lorentz spacetimes of constant curvature'' [Geom. Dedicata 126 (2007), 3--45; MR2328921] by G. MessAndersson, Lars; Barbot, Thierry; Benedetti, Riccardo et alin Geometriae Dedicata (2007), 126Detailed reference viewed: 208 (1 UL) Minimal surfaces and particles in 3-manifoldsKrasnov, Kirill; Schlenker, Jean-Marc in Geometriae Dedicata (2007), 126Detailed reference viewed: 144 (0 UL) 1