The Experts below are selected from a list of 16848 Experts worldwide ranked by ideXlab platform
Stephan Tillmann - One of the best experts on this subject based on the ideXlab platform.
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tessellating the moduli space of Strictly Convex projective structures on the once punctured torus
Experimental Mathematics, 2019Co-Authors: Robert C. Haraway, Stephan TillmannAbstract:ABSTRACTWe show that associating the Euclidean cell decomposition due to Cooper and Long to each point of the moduli space of marked Strictly Convex real projective structures of finite volume on t...
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an algorithm for the euclidean cell decomposition of a cusped Strictly Convex projective surface
Journal of Computational Geometry, 2016Co-Authors: Stephan Tillmann, Sampson WongAbstract:Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic $n$–manifolds of finite volume to non-compact Strictly Convex projective $n$–manifolds of finite volume. We show that Weeks' algorithm to compute this decomposition for a hyperbolic surface generalises to Strictly Convex projective surfaces.
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Tessellating the moduli space of Strictly Convex projective structures on the once-punctured torus
arXiv: Geometric Topology, 2015Co-Authors: Robert C. Haraway, Stephan TillmannAbstract:We show that associating the Euclidean cell decomposition due to Cooper and Long to each point of the moduli space of framed Strictly Convex real projective structures of finite volume on the once-punctured torus gives this moduli space a natural cell decomposition. The proof makes use of coordinates due to Fock and Goncharov, the action of the mapping class group as well as algorithmic real algebraic geometry. We also show that the decorated moduli space of framed Strictly Convex real projective structures of finite volume on the thrice-punctured sphere has a natural cell decomposition.
Günter Rote - One of the best experts on this subject based on the ideXlab platform.
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Strictly Convex drawings of planar graphs
Documenta Mathematica, 2006Co-Authors: Imre Bárány, Günter RoteAbstract:Every three-connected planar graph with n vertices has a drawing on an O(n(2)) x O(n(2)) grid in which all faces are Strictly Convex polygons. These drawings are obtained by perturbing (not Strictly) Convex drawings on O(n) x O(n) grids. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.
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Strictly Convex drawings of planar graphs
Symposium on Discrete Algorithms, 2005Co-Authors: Günter RoteAbstract:Every three-connected planar graph with n vertices has a drawing on an O(n7/3) × O(n7/3) grid in which all faces are Strictly Convex polygons.
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SODA - Strictly Convex drawings of planar graphs
2005Co-Authors: Günter RoteAbstract:Every three-connected planar graph with n vertices has a drawing on an O(n7/3) × O(n7/3) grid in which all faces are Strictly Convex polygons.
Mickaël Crampon - One of the best experts on this subject based on the ideXlab platform.
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Entropies of Strictly Convex projective manifolds
Journal of Modern Dynamics, 2009Co-Authors: Mickaël CramponAbstract:Let $M$ be a compact manifold of dimension $n$ with a Strictly Convex projective structure. We consider the geodesic flow of the Hilbert metric on it, which is known to be Anosov. We prove that its topological entropy is less than $n-1$, with equality if and only if the structure is Riemannian hyperbolic. As a corollary, the volume entropy of a divisible Strictly Convex set is less than $n-1$, with equality if and only if it is an ellipsoid.
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Entropies of compact Strictly Convex projective manifolds
Journal of modern dynamics, 2009Co-Authors: Mickaël CramponAbstract:Let M be a compact manifold of dimension n with a Strictly Convex projective structure. We consider the geodesic flow of the Hilbert metric on it, which is known to be Anosov. We prove that its topological entropy is less than n-1, with equality if and only if the structure is Riemannian, that is hyperbolic. As a corollary, we get that the volume entropy of a divisible Strictly Convex set is less than n-1, with equality if and only if it is an ellipsoid.
Moonjin Kang - One of the best experts on this subject based on the ideXlab platform.
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L2-type contraction for shocks of scalar viscous conservation laws with Strictly Convex flux
Journal de Mathématiques Pures et Appliquées, 2021Co-Authors: Moonjin KangAbstract:Abstract We study the L 2 -type contraction property of large perturbations around shock waves of scalar viscous conservation laws with Strictly Convex fluxes in one space dimension. The contraction holds up to a shift, and it is measured by a weighted relative entropy, for which we choose an appropriate entropy associated with the Strictly Convex flux. In particular, we handle shocks with small amplitude. This result improves the recent article [19] of the author and Vasseur on L 2 -contraction property of shocks to scalar viscous conservation laws with a special flux, that is almost the Burgers flux.
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l 2 type contraction for shocks of scalar viscous conservation laws with Strictly Convex flux
arXiv: Analysis of PDEs, 2019Co-Authors: Moonjin KangAbstract:We study the $L^2$-type contraction property of large perturbations around shock waves of scalar viscous conservation laws with Strictly Convex fluxes in one space dimension. The contraction holds up to a shift, and it is measured by a weighted related entropy, for which we choose an appropriate entropy associated with the Strictly Convex flux. In particular, we handle shocks with small amplitude. This result improves the recent article [18] of the author and Vasseur on $L^2$-contraction property of shocks to scalar viscous conservation laws with a special flux, that is almost the Burgers flux.
Patrick Roome - One of the best experts on this subject based on the ideXlab platform.
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Two examples of non Strictly Convex large deviations
arXiv: Probability, 2014Co-Authors: Stefano De Marco, Antoine Jacquier, Patrick RoomeAbstract:We present two examples of a large deviations principle where the rate function is not Strictly Convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non Strictly Convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.
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Two examples of non Strictly Convex large deviations
SSRN Electronic Journal, 2014Co-Authors: Stefano De Marco, Antoine Jacquier, Patrick RoomeAbstract:We present here two examples of a large deviations principle where the rate function is not Strictly Convex. This is motivated by an example from mathematical finance, and adds a new item to the zoology of non Strictly Convex large deviations. For one of these examples, we also show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.
