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Mathematische Annalen, ISSN 0025-5831, 8/2016, Volume 365, Issue 3, pp. 1425 - 1498
In this paper we prove necessary and sufficient conditions for the Kobayashi metric on a convex domain to be Gromov hyperbolic. In particular we show that for... 
32F18 | Mathematics, general | Mathematics | 53C23 | 32F45 | MATHEMATICS | PSEUDOCONVEX DOMAINS
Journal Article
Mathematische annalen, ISSN 1432-1807, 2018, Volume 373, Issue 1-2, pp. 155 - 163
We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial... 
53C20 | Mathematics, general | Mathematics | 53C23 | 58E20 | MATHEMATICS | CURVATURE
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2016, Volume 293, pp. 436 - 528
We relate generalized Lebesgue decompositions of measures in terms of curve fragments (“Alberti representations”) and Weaver derivations. This correspondence... 
Lipschitz algebra | Derivation | Measurable differentiable structure | 46J15 | 58C20 | 53C23 | POROSITY | MATHEMATICS | DIFFERENTIABILITY | SETS
Journal Article
Journal of differential geometry, ISSN 0022-040X, 1990, Volume 32, Issue 1, pp. 269 - 298
Journal Article
Nagoya Mathematical Journal, ISSN 0027-7630, 09/2012, Volume 207, pp. 95 - 138
In this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space of p -Dirichlet finite functions on... 
53C23 | 05C63 | 31C20
Journal Article
Forum Mathematicum, ISSN 0933-7741, 01/2018, Volume 30, Issue 1, pp. 159 - 170
We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on... 
Hilbert metric | 53C23 | complex geodesics | (non-)Gromov hyperbolic | (Convex) tube domains | 32F45 | 32A07 | (Non-)Gromov hyperbolic | Complex geodesics | MATHEMATICS | MATHEMATICS, APPLIED | GROMOV HYPERBOLICITY | Domains | Geodesy
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2017, Volume 369, Issue 3, pp. 1557 - 1571
In his seminal work about bounded cohomology, Gromov showed that, under some topological conditions, every closed Riemannian manifold of small volume has large... 
Secondary 53C20 | Mathematics, general | Mathematics | Primary 53C23 | MATHEMATICS | RIEMANNIAN-MANIFOLDS
Journal Article
Geometric and functional analysis, ISSN 1420-8970, 2007, Volume 17, Issue 5, pp. 1551 - 1620
We introduce and examine a special class of cube complexes. We show that special cube-complexes virtually admit local isometries to the standard 2-complexes of... 
20F65 | 53C23 | Analysis | CAT cube complexes | residual finiteness | Mathematics | right-angled Artin groups | 20F36 | 20E26 | 20F67 | 20F55 | Residual finiteness | Right-angled Artin groups | MATHEMATICS | FINITE | POLYGONS | SUBGROUP SEPARABILITY | COXETER GROUPS | GRAPHS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 6/2015, Volume 176, Issue 1, pp. 175 - 183
K-area is an invariant for Riemannian manifolds introduced by Gromov as an obstruction to the existence of positive scalar curvature. However in general it is... 
Geometry | Scalar curvature | Vector bundle | 53C23 | Surgery | Mathematics | K-area | MATHEMATICS
Journal Article
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645, 04/2019, Volume 71, Issue 2, pp. 635 - 650
For a metric measure space, we consider the set of distributions of 1-Lipschitz functions, which is called the 1-measurement. On the 1-measurement, we have the... 
MATHEMATICS | 1-measurement | Lipschitz order | isoperimetric inequality | observable diameter | metric measure space
Journal Article
manuscripta mathematica, ISSN 0025-2611, 11/2019, Volume 160, Issue 3, pp. 411 - 481
We define functionals generalising the Seiberg–Witten functional on closed $$spin^c$$ s p i n c manifolds, involving higher order derivatives of the curvature... 
Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C23 | 53C21 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 53C07 | EXISTENCE | MATHEMATICS | DUALITY
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 08/2019, Volume 69, Issue 4, pp. 931 - 938
In this paper, we show that a class of metric spaces determined by a continuous function , which defines on the metric space of all real, × -matrices is closed... 
Gromov hyperbolicity | Secondary 53C23 | Gromov-Hausdorff distance | Primary 51F99 | Gromov hyperbolic space | MATHEMATICS | Metric space | Continuity (mathematics) | Convergence
Journal Article
Manuscripta mathematica, ISSN 1432-1785, 2018, Volume 160, Issue 1-2, pp. 187 - 198
We give a characterisation of Bieberbach manifolds which are geodesic boundaries of a compact flat manifold, and discuss the low dimensional cases, up to... 
Geometry | 53C20 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C23 | 53C22 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | MATHEMATICS | Musical groups
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2017, Volume 49, Issue 4, pp. 690 - 693
We answer a question of M. Gromov on the waist of the unit ball. 
53C23 (primary) | 49Q20 | MATHEMATICS | MAPS | SPHERE | Mathematics - Metric Geometry
Journal Article
Geometriae dedicata, ISSN 1572-9168, 2014, Volume 177, Issue 1, pp. 367 - 384
A geodesic bicombing on a metric space selects for every pair of points a geodesic connecting them. We prove existence and uniqueness results for geodesic... 
Geometry | 20F65 | Geodesic bicombing | Injective hull | 53C23 | Hyperbolic group | Mathematics | Tight span | Absolute retract | 20F67 | MATHEMATICS | METRIC-SPACES
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 6/2019, Volume 200, Issue 1, pp. 105 - 114
Let $$\gamma ^n_k\rightarrow G_k(\mathbb {H}^n)$$ γ k n → G k ( H n ) be the Stiefel bundle of quaternionic k-frames in $$\mathbb {H}^n$$ H n over the the... 
Connections | Quaternionic Grassmannians | 53C42 | 58J99 | 53C23 | 53C05 | Mathematics | Topology | Principal bundles | Convex and Discrete Geometry | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Differential Geometry | Symplectic Pontrjagin forms
Journal Article
Calculus of variations and partial differential equations, ISSN 1432-0835, 2011, Volume 44, Issue 3-4, pp. 477 - 494
We prove local Poincaré inequalities under various curvature-dimension conditions which are stable under the measured Gromov–Hausdorff convergence. The first... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Theoretical, Mathematical and Computational Physics | Analysis | Secondary 28A33 | Mathematics | Primary 53C23 | 49Q20 | MATHEMATICS | MATHEMATICS, APPLIED | DISPLACEMENT CONVEXITY | GRADIENT FLOWS | RICCI CURVATURE | GEOMETRY
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 10, pp. 1927 - 1942
We consider the corresponding Christoffel-Minkowski problem for curvature measures. The existence of star-shaped (n-k)-convex bodies with prescribed kth... 
MATHEMATICS | MINKOWSKI PROBLEM | ELLIPTIC-EQUATIONS | DIFFERENTIAL GEOMETRY | 53C42 | 53C23 | 35J60
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 2/2016, Volume 180, Issue 1, pp. 323 - 338
For a non-vanishing gradient-like vector field on a compact manifold $$X^{n+1}$$ X n + 1 with boundary, a discrete set of trajectories may be tangent to the... 
Geometry | 57N80 | Amenable group | 53C23 | Mathematics | 58K45 | Simplicial volume | Simplicial norm | Traversing vector field | MATHEMATICS
Journal Article
Duke mathematical journal, ISSN 0012-7094, 2012, Volume 161, Issue 13, pp. 2549 - 2603
We consider several ways to measure the "geometric complexity" of an embedding from a simplicial complex into Euclidean space. One of these is a version of... 
MATHEMATICS | KNOTS | VOLUME | CONJECTURE | SURFACES | Mathematics - Geometric Topology | 53C23 | 53C99
Journal Article
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