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ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2017, Volume 36, Issue 4, pp. 1 - 15
We present a method for locally injective seamless parametrization of triangular mesh surfaces of arbitrary genus, with or without boundaries, given desired... 
injective maps | discrete harmonic | global parametrization | mesh parametrization | Mesh parametrization | Global parametrization | Discrete harmonic | Injective maps | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PARAMETERIZATION | MAPPINGS
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 4/2019, Volume 29, Issue 2, pp. 1075 - 1108
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 10/2019, Volume 202, Issue 1, pp. 203 - 211
An n-dimensional Bieberbach group is the fundamental group of a closed flat n-dimensional manifold. K. Dekimpe and P. Penninckx conjectured that an... 
Bieberbach group | Cyclic group | Crystallographic group | Convex and Discrete Geometry | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Generators | Projective Geometry | Topology | Differential Geometry | MATHEMATICS | NUMBER
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 1/2019, Volume 29, Issue 1, pp. 33 - 82
Journal Article
Quarterly Journal of Mathematics, ISSN 0033-5606, 12/2016, Volume 67, Issue 4, pp. 743 - 755
Let G be a connected complex Lie group or a connected amenable Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a... 
MATHEMATICS | DISCRETE STRUCTURE GROUP | VECTOR BUNDLES | SOLVABLE HOLONOMY | Mathematics
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 1/2015, Volume 25, Issue 1, pp. 281 - 297
An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N 6 can be defined as a pair of a 2-form ω and a 3-form ρ. We prove that any analytic SU(3)- or... 
Exceptional holonomy | 53C44 | 53C10 | Mathematics | Stable forms | 53C29 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hitchin’s flow equation | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | SPIN | METRICS | MANIFOLDS | Hitchin's flow equation | SU/U | Resveratrol
Journal Article
ACM Transactions on Graphics, ISSN 0730-0301, 08/2008, Volume 27, Issue 3, p. 1
We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of... 
Rods | Discrete differential geometry | Strands | Discrete holonomy | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NUMBER | INSTABILITY | DYNAMICS | rods | discrete differential geometry | discrete holonomy | SIMULATION | strands
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 3139 - 3170
In this paper, a metric with $$\hbox {G}_2$$ G 2 holonomy and slow rate of convergence to the cone metric is constructed on a ball inside the cone over the... 
Abstract Harmonic Analysis | Special holonomy | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Ricci-flat | Mathematics | 53C25 | Differential Geometry | Dynamical Systems and Ergodic Theory | G_2 holonomy | 53C29
Journal Article
JOURNAL OF HIGH ENERGY PHYSICS, ISSN 1029-8479, 03/2018, Issue 3
We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G(2) manifolds. For a given G(2)... 
SUPERSYMMETRY | FANO 3-FOLDS | FIELD-THEORIES | SINGULARITIES | String Duality | DISCRETE TORSION | 3 DIMENSIONS | Supersymmetry and Duality | EXCEPTIONAL HOLONOMY MANIFOLDS | SUBMANIFOLDS | THEORY COMPACTIFICATIONS | SURFACES | PHYSICS, PARTICLES & FIELDS
Journal Article
Nuclear Physics, Section B, ISSN 0550-3213, 1998, Volume 524, Issue 1, pp. 269 - 282
We consider Type II string theories on T-n/Z(2)(m) Joyce orbifolds. This class contains orbifolds which can be desingularised to give manifolds of G(2) (n = 7)... 
DUALITY | ORBIFOLDS | COMPACT RIEMANNIAN 7-MANIFOLDS | DISCRETE TORSION | D-BRANES | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2007, Volume 44, Issue 3, pp. 615 - 626
A pair of pants Sigma (0, 3) is a building block of oriented surfaces. The purpose of this paper is to determine the discrete conditions for the holonomy group... 
A pair of pants | Hyperbolic structure | Hyperbolic matrix | Discrete holonomy group | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | a pair of pants | hyperbolic matrix | hyperbolic structure | discrete holonomy group
Journal Article
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 6/2019, Volume 200, Issue 1, pp. 93 - 103
We prove that the holonomy map from the set of equivalence classes of parabolic complex projective structures on compact surfaces with finitely many punctures... 
Holonomy map | 37F75 | 34M35 | Mathematics | 34M45 | Topology | Foliations | Convex and Discrete Geometry | Algebraic Geometry | Complex projective structures | Hyperbolic Geometry | Projective Geometry | Differential Geometry
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 10/2015, Volume 25, Issue 4, pp. 2687 - 2697
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2014, Volume 51, Issue 2, pp. 403 - 426
The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere Sigma(0, 3), a one-holed torus... 
Discrete holonomy group | Involution | Fricke space | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | involution | discrete holonomy group
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2019, Volume 29, Issue 3, pp. 2147 - 2216
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2012, Volume 255, Issue 1, pp. 1 - 23
In the spirit of the Goodman-Plante average condition for the existence of a transverse invariant measure for foliations, we give an averaging condition to... 
Lamination | Discrete equivalence relation | Measure | MATHEMATICS | lamination | measure | FOLIATIONS | HOLONOMY | DYNAMICS | MANIFOLDS | discrete equivalence relation | Mathematics
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2206 - 2224
Journal Article
Geometry and Topology, ISSN 1465-3060, 08/2017, Volume 21, Issue 5, pp. 3047 - 3092
We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that... 
MATHEMATICS | BUNDLES | FOLIATIONS | STABILITY | HOLONOMY | MORITA-MUMFORD CLASSES | MANIFOLDS | MAPPING CLASS GROUP | HOMOTOPY | MODULI SPACES
Journal Article
Journal Article
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