scholarly journals Renormalized volume and the volume of the convex core

2017 ◽  
Vol 67 (5) ◽  
pp. 2083-2098
Author(s):  
Martin Bridgeman ◽  
Richard Canary
Keyword(s):  
Convex Core

scholarly journals Geodesic planes in geometrically finite acylindrical -manifolds

2021 ◽  
pp. 1-40
Author(s):  
YVES BENOIST ◽  
HEE OH
Keyword(s):  
Closed Geodesic ◽  
Duke Math ◽  
Geometrically Finite ◽  
Convex Cocompact ◽  
Invent Math ◽  
Convex Core

Abstract Let M be a geometrically finite acylindrical hyperbolic $3$ -manifold and let $M^*$ denote the interior of the convex core of M. We show that any geodesic plane in $M^*$ is either closed or dense, and that there are only countably many closed geodesic planes in $M^*$ . These results were obtained by McMullen, Mohammadi and Oh [Geodesic planes in hyperbolic 3-manifolds. Invent. Math.209 (2017), 425–461; Geodesic planes in the convex core of an acylindrical 3-manifold. Duke Math. J., to appear, Preprint, 2018, arXiv:1802.03853] when M is convex cocompact. As a corollary, we obtain that when M covers an arithmetic hyperbolic $3$ -manifold $M_0$ , the topological behavior of a geodesic plane in $M^*$ is governed by that of the corresponding plane in $M_0$ . We construct a counterexample of this phenomenon when $M_0$ is non-arithmetic.

Convex cores of measures on R d

2001 ◽  
Vol 38 (1-4) ◽  
pp. 177-190 ◽  
Author(s):  
Imre Csiszár ◽  
F. Matúš
Keyword(s):  
Borel Measure ◽  
Convex Sets ◽  
Probability Measures ◽  
Countable Number ◽  
Borel Sets ◽  
Finite Borel Measure ◽  
Number Of Faces ◽  
Convex Core

We define the convex core of a finite Borel measure Q on R d as the intersection of all convex Borel sets C with Q(C) =Q(R d). It consists exactly of means of probability measures dominated by Q. Geometric and measure-theoretic properties of convex cores are studied, including behaviour under certain operations on measures. Convex cores are characterized as those convex sets that have at most countable number of faces.

scholarly journals Convexity in complex networks

2018 ◽  
Vol 6 (2) ◽  
pp. 176-203 ◽  
Author(s):  
TILEN MARC ◽  
LOVRO ŠUBELJ
Keyword(s):  
Complex Networks ◽  
Geodesic Distance ◽  
Connected Subgraph ◽  
Geodesic Path ◽  
Connected Subset ◽  
Social Collaboration ◽  
Graph Properties ◽  
Definition Of ◽  
Locally Convex ◽  
Convex Core

AbstractMetric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes induces a convex subgraph. We show that convexity is an inherent property of many networks that is not present in a random graph. Most convex are spatial infrastructure networks and social collaboration graphs due to their tree-like or clique-like structure, whereas the food web is the only network studied that is truly non-convex. Core–periphery networks are regionally convex as they can be divided into a non-convex core surrounded by a convex periphery. Random graphs, however, are only locally convex meaning that any connected subgraph of size smaller than the average geodesic distance between the nodes is almost certainly convex. We present different measures of network convexity and discuss its applications in the study of networks.

Fingerprint indexing based on minutiae pairs and convex core point

2017 ◽  
Vol 67 ◽  
pp. 110-126 ◽  
Author(s):  
Javad Khodadoust ◽  
Ali Mohammad Khodadoust
Keyword(s):  
Core Point ◽  
Fingerprint Indexing ◽  
Convex Core

scholarly journals Geodesics in Margulis spacetimes

2011 ◽  
Vol 32 (2) ◽  
pp. 643-651 ◽  
Author(s):  
WILLIAM M. GOLDMAN ◽  
FRANÇOIS LABOURIE
Keyword(s):  
Compact Convex ◽  
Hyperbolic Surface ◽  
Orbit Equivalence ◽  
Closed Geodesics ◽  
Timelike Geodesic ◽  
Convex Core

AbstractLet M3 be a Margulis spacetime whose associated complete hyperbolic surface Σ2 has a compact convex core. Generalizing the correspondence between closed geodesics on M3 and closed geodesics on Σ2, we establish an orbit equivalence between recurrent spacelike geodesics on M3 and recurrent geodesics on Σ2. In contrast, no timelike geodesic recurs in either forward or backward time.

scholarly journals Geodesically Complete Hyperbolic Structures

2017 ◽  
Vol 166 (2) ◽  
pp. 219-242
Author(s):  
ARA BASMAJIAN ◽  
DRAGOMIR ŠARIĆ
Keyword(s):  
Teichmüller Space ◽  
Hyperbolic Surface ◽  
Teichmuller Space ◽  
Geometric Proof ◽  
Hyperbolic Structures ◽  
Infinite Type ◽  
Length Spectrum Metric ◽  
Geodesically Complete ◽  
The Relationship ◽  
Convex Core

AbstractIn the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we give a geometric proof of a Theorem due to Alvarez and Rodriguez that a geodesically complete hyperbolic surface is made up of its convex core with funnels attached along the simple closed geodesic components and half-planes attached along simple open geodesic components. We next consider gluing infinitely many pairs of pants along their cuffs to obtain an infinite hyperbolic surface. We prove that there always exists a choice of twists in the gluings such that the surface is complete regardless of the size of the cuffs. This generalises the examples of Matsuzaki.In the second part we consider complete hyperbolic flute surfaces with rapidly increasing cuff lengths and prove that the corresponding quasiconformal Teichmüller space is incomplete in the length spectrum metric. Moreover, we describe the twist coordinates and convergence in terms of the twist coordinates on the closure of the quasiconformal Teichmüller space.

Convex-Core Model of Molecules in Crystalline State

1959 ◽  
Vol 14 (3) ◽  
pp. 247-252 ◽  
Author(s):  
Taro Kihara ◽  
Saburo Koba
Keyword(s):  
Crystalline State ◽  
Core Model ◽  
Convex Core

The Second Virial Coefficients of n-Alkanes and Their Mixtures from the Kihara Convex Core Intermolecular Pair Potential

1993 ◽  
Vol 58 (10) ◽  
pp. 2489-2504 ◽  
Author(s):  
Jan Pavlíček ◽  
Karel Aim ◽  
Tomáš Boublík
Keyword(s):  
Geometric Mean ◽  
Second Virial Coefficient ◽  
Pair Potential ◽  
Virial Coefficients ◽  
Liquid Density ◽  
Second Virial Coefficients ◽  
Uncertainty Estimates ◽  
Pure Compounds ◽  
The Individual ◽  
Convex Core

The second virial coefficients for a series of C2 to C8 n-alkanes and the second virial cross coefficients for their binary mixtures were calculated as a function of temperature from the exact expressions derived for the Kihara rod-like molecules. The three parameters of Kihara pair potential, ε/k, σ and l for the individual compounds were either used as determined from vapour-liquid equilibrium and saturated liquid density data in a previous study or with ε/k adjusted to the second virial coefficient data. The results are accurate almost within experimental uncertainty estimates of the data. In the case of mixtures the second virial cross coefficients were calculated from a similar expression in which only the ε12/k parameter was adjusted whereas σ12 = (σ1 + σ2)/2 and l1 and l2 of pure compounds were employed. It appears that the correction factor to the geometric mean combining rule for ε12/k is always less than and close to unity. Comparison with the values obtained from the Tsonopoulos generalized correlation reveals fair agreement between the characteristic binary k12 parameters from the two methods.

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