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Minimal Lagrangian diffeomorphisms between hyperbolic cone surfaces and Anti-de Sitter geometry Toulisse, Jérémy Presentation (2015, July 13) We study minimal diffeomorphisms between hyperbolic cone-surfaces (that is diffeomor- phisms whose graph are minimal submanifolds). We prove that, given two hyperbolic metrics with the same number of ... [more ▼] We study minimal diffeomorphisms between hyperbolic cone-surfaces (that is diffeomor- phisms whose graph are minimal submanifolds). We prove that, given two hyperbolic metrics with the same number of conical singularities of angles less than π, there always exists a minimal diffeomorphism isotopic to the identity. When the cone-angles of one metric are strictly smaller than the ones of the other, we prove that this diffeomorphism is unique. When the angles are the same, we prove that this diffeomorphism is unique and area- preserving (so is minimal Lagrangian). The last result is equivalent to the existence of a unique maximal space-like surface in some Globally Hyperbolic Maximal (GHM) anti-de Sitter (AdS) 3-manifold with particles. [less ▲] Detailed reference viewed: 67 (10 UL)Minimal diffeomorphism between hyperbolic surfaces with cone singularities Toulisse, Jérémy E-print/Working paper (2014) We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces (Σ,g1) and (Σ,g2) when the cone angles of g1 and g2 are different and smaller than π. When ... [more ▼] We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces (Σ,g1) and (Σ,g2) when the cone angles of g1 and g2 are different and smaller than π. When the cone angles of g1 are strictly smaller than the ones of g2, this minimal diffeomorphism is unique. [less ▲] Detailed reference viewed: 88 (2 UL)Irreducible decomposition for local representations of quantum Teichmüller space Toulisse, Jérémy E-print/Working paper (2014) We give an irreducible decomposition of the so-called local representations \cite{math/0407086} of the quantum Teichmüller space $\mathcal{T}_q(\Sigma)$ where $\Sigma$ is a punctured surface of genus $g>0 ... [more ▼] We give an irreducible decomposition of the so-called local representations \cite{math/0407086} of the quantum Teichmüller space $\mathcal{T}_q(\Sigma)$ where $\Sigma$ is a punctured surface of genus $g>0$ and $q$ is a $N$-th root of unity with $N$ odd. [less ▲] Detailed reference viewed: 88 (3 UL)Maximal Surface in AdS convex GHM 3-manifold with particles Toulisse, Jérémy E-print/Working paper (2013) We prove the existence of a unique maximal surface in an anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (i.e. with conical singularities along timelike lines) for ... [more ▼] We prove the existence of a unique maximal surface in an anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (i.e. with conical singularities along timelike lines) for cone-angles less than $\pi$. We reinterpret this result in terms of Teichm\"uller theory, and prove the existence of a unique minimal Lagrangian diffeomorphism isotopic to the identity between two hyperbolic structures with conical singularities of the same angles on a closed surface with marked points. [less ▲] Detailed reference viewed: 56 (3 UL)The $n$-th prime asymptotically ; Toulisse, Jérémy in Journal de Théorie des Nombres de Bordeaux (2013) A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the compu- tation of its terms is also given, which will be an improvement of that by Salvy (1994 ... [more ▼] A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the compu- tation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $li−1 (n)$, after having re- tained the first $m$ terms, for $1 ≤ m ≤ 11$, are given. Finally, as- suming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n ≥ r_3$ , we have $p_n > s_3 (n)$ where $s_3 (n)$ is the sum of the first four terms of the asymptotic expansion. [less ▲] Detailed reference viewed: 139 (0 UL) |
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