scholarly journals Hyperbolic surfaces with long systoles that form a pants decomposition

2017 ◽  
Vol 146 (3) ◽  
pp. 1069-1081 ◽  
Author(s):  
Bram Petri
Keyword(s):  
Hyperbolic Surfaces ◽  
Pants Decomposition

Geometric Schottky groups and non-compact hyperbolic surfaces with infinite genus

2021 ◽  
Vol 76 ◽  
pp. 101752
Author(s):  
John A. Arredondo ◽  
Camilo Ramírez Maluendas
Keyword(s):  
Schottky Groups ◽  
Hyperbolic Surfaces

scholarly journals 3D B-Rep meshing for real-time data-based geometric parametric analysis

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Tristan Maquart ◽  
Thomas Elguedj ◽  
Anthony Gravouil ◽  
Michel Rochette
Keyword(s):  
Real Time ◽  
Surface Topology ◽  
Time Data ◽  
Standard Data ◽  
Input Surface ◽  
Cad Models ◽  
Pants Decomposition ◽  
Parametric Studies ◽  
Geometry Feature ◽  
Complicated Geometry

AbstractThis paper presents an effective framework to automatically construct 3D quadrilateral meshes of complicated geometry and arbitrary topology adapted for parametric studies. The input is a triangulation of the solid 3D model’s boundary provided from B-Rep CAD models or scanned geometry. The triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. This workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. This set of cuboids perfectly replicates the input surface topology. Using aligned global parameterization, patches are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. Based on the cuboid decomposition and global parameterization, a 3D quadrilateral mesh is extracted. For different parametric instances with the same topology but different geometries, the MEG-IsoQuad method allows to have the same representation: isotopological meshes holding the same connectivity where each point on a mesh has an analogous one into all other meshes. Faithful 3D numerical charts of parametric geometries are then built using standard data-based techniques. Geometries are then evaluated in real-time. The efficiency and the robustness of the proposed approach are illustrated through a few parametric examples.

scholarly journals Hyperbolic three-string vertex

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Atakan Hilmi Fırat
Keyword(s):  
Boundary Value Problem ◽  
Conservation Laws ◽  
Riemann Surfaces ◽  
Higher Order ◽  
Local Coordinates ◽  
Pants Decomposition ◽  
Fuchsian Equation ◽  
String Amplitudes ◽  
Hyperbolic Riemann Surfaces ◽  
Liouville’S Equation

Abstract We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville’s equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.

Asymptotic Estimates of the First Eigenvalue of the p-Laplacian

2003 ◽  
Vol 3 (2) ◽  
Author(s):  
Bruno Colbois ◽  
Ana-Maria Matei
Keyword(s):  
Direct Application ◽  
Parameter Family ◽  
Precise Estimate ◽  
First Eigenvalue ◽  
Asymptotic Estimates ◽  
Hyperbolic Surfaces ◽  
The First Eigenvalue

AbstractWe consider a 1-parameter family of hyperbolic surfaces M(t) of genus ν which degenerate as t → 0 and we obtain a precise estimate of λAs a direct application, we obtain that the quotientTo prove our results we use in an essential way the geometry of hyperbolic surfaces which is very well known. We show that an eigenfunction for λ

scholarly journals Isometry groups of infinite-genus hyperbolic surfaces

2021 ◽  
Author(s):  
Tarik Aougab ◽  
Priyam Patel ◽  
Nicholas G. Vlamis
Keyword(s):  
Hyperbolic Surfaces ◽  
Isometry Groups

scholarly journals Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces

2005 ◽  
pp. 483-515 ◽  
Author(s):  
David Borthwick ◽  
Chris Judge ◽  
Peter Perry
Keyword(s):  
Zeta Function ◽  
Spectral Geometry ◽  
Hyperbolic Surfaces ◽  
Geometrically Finite ◽  
Selberg’S Zeta Function

Hyperbolic surfaces

1997 ◽  
pp. 49-77
Author(s):  
Christoph Hummel
Keyword(s):  
Hyperbolic Surfaces

scholarly journals On the minimal diameter of closed hyperbolic surfaces

2020 ◽  
Author(s):  
Thomas Budzinski ◽  
Nicolas Curien ◽  
Bram Petri
Keyword(s):  
Hyperbolic Surfaces ◽  
Minimal Diameter

scholarly journals Equality in László Fejes Tóth’s triangle bound for hyperbolic surfaces

2011 ◽  
Vol 77 (3-4) ◽  
pp. 669-679
Author(s):  
Christophe Bavard ◽  
Károly J. Böröczky ◽  
Borbála Farkas ◽  
István Prok ◽  
Lluis Vena ◽  
...  
Keyword(s):  
Hyperbolic Surfaces
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