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1995, DMV Seminar, ISBN 3764352426, Volume Bd. 25, v, 112
Book
Journal Article
Advances in Mathematics, ISSN 0001-8708, 07/2018, Volume 332, pp. 287 - 310
Botelho, Jamison, and Molnár [1], and Gehér and Šemrl [4] have recently described the general form of surjective isometries of Grassmann spaces of all projections of a fixed finite rank on a Hilbert space H... 
Subspace | Projection | Isometry | Geodesic structure | Grassmann space | Gap metric | MATHEMATICS | SET | N-DIMENSIONAL SUBSPACES | TRANSFORMATIONS
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2017, Volume 31, Issue 3, pp. 2015 - 2038
We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all ultrametrics. The CAT(0... 
Polytope | Phylogenetic tree | CAT space | Geodesic triangle | Ultrametric | Tropical convexity | Billera-Holmes-Vogtman metric | MATHEMATICS, APPLIED | phylogenetic tree | APPROXIMATION | COMPLEXES | ALGORITHM | tropical convexity | SEMIMODULES | PHYLOGENETIC TREES | ultrametric | geodesic triangle | polytope | GEOMETRY
Journal Article
Potential Analysis, ISSN 0926-2601, 2/2012, Volume 36, Issue 2, pp. 317 - 337
... ≤ 2 in proper geodesic metric spaces. By means of a general Hamilton–Jacobi semigroup we prove that these are equivalent, and moreover equivalent to the hypercontractivity of the Hamilton–Jacobi semigroup... 
Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY
Journal Article
Pattern Recognition, ISSN 0031-3203, 12/2016, Volume 60, pp. 802 - 812
The sample mean is one of the most fundamental concepts in statistics. Properties of the sample mean that are well-defined in Euclidean spaces become unclear in graph spaces... 
Majorize–minimize algorithm | Geometric midpoint | Graph edit distance | Fréchet mean | Consistent estimator | Graph matching | Majorize-minimize algorithm | MANIFOLDS | Frechet mean | COMPUTATION | ANALYSIS GEODESIC PCA | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Algorithms
Journal Article
Journal of the Royal Statistical Society: Series B (Statistical Methodology), ISSN 1369-7412, 03/2017, Volume 79, Issue 2, pp. 463 - 482
Journal Article
ACM TRANSACTIONS ON GRAPHICS, ISSN 0730-0301, 07/2007, Volume 26, Issue 3
.... Shapes - triangular meshes or more generally straight line graphs in Euclidean space - are treated as points in a shape space... 
Riemannian geometry | GEODESIC PATHS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | geodesic | parallel transport | PARAMETERIZATION | isometric | shape exploration | deformation | shape space
Journal Article
Communications in mathematical physics, ISSN 1432-0916, 2018, Volume 364, Issue 2, pp. 441 - 504
We show that a shift space on a finite alphabet with a non-uniform specification property can be modeled by a strongly positive recurrent countable-state Markov shift to which every equilibrium state lifts... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | THERMODYNAMIC FORMALISM | UNIQUE EQUILIBRIUM STATES | GEODESIC-FLOWS | MAPS | INTRINSIC ERGODICITY | SYSTEMS | PIECEWISE MONOTONIC TRANSFORMATIONS | BETA-SHIFTS | PHYSICS, MATHEMATICAL | SYMBOLIC DYNAMICS | ENTROPY
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2007, Volume 26, Issue 3, pp. 64 - es
.... Shapes -- triangular meshes or more generally straight line graphs in Euclidean space -- are treated as points in a shape space... 
Riemannian geometry | geodesic | parallel transport | shape space | isometric deformation | shape exploration | Geodesic | Shape space | Shape exploration | Isometric deformation | Parallel transport
Journal Article
by Wu, WS
Ergodic theory and dynamical systems, ISSN 0143-3857, 07/2020, Volume 40, Issue 7, pp. 1991 - 2016
We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald... 
MATHEMATICS | MATHEMATICS, APPLIED | Berwald spaces | non-positive flag curvature | CURVATURE | higher rank rigidity | MANIFOLDS | geodesic flow | Finsler spaces | Minkowski space | Rigidity
Journal Article
by Wu, Yan and Qi, Yi
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 1, pp. 154 - 166
The angular geometry of asymptotic Teichmüller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of AT(X... 
Geodesic | Teichmüller space | Asymptotic Teichmüller space | Angle | MATHEMATICS | MATHEMATICS, APPLIED | Teichmuller space | Asymptotic Teichmuller space
Journal Article
Annals of global analysis and geometry, ISSN 1572-9060, 2019, Volume 56, Issue 3, pp. 597 - 611
Journal Article
Journal of mathematical imaging and vision, ISSN 1573-7683, 2014, Volume 50, Issue 1-2, pp. 60 - 97
Journal Article
Studia Logica, ISSN 0039-3215, 06/2017, Volume 105, Issue 3, pp. 611 - 624
.... In this paper we adapt this to the class of CAT)-spaces X for and establish a new metatheorem that explains specific bound extractions that recently have been achieved... 
CAT(κ) -spaces | Effective bounds | Proof mining | MATHEMATICS | GEODESIC SPACES | PHILOSOPHY | FUNCTIONAL-ANALYSIS | CAT(kappa)-spaces | LOGICAL METATHEOREMS | LOGIC | Mineral industry | Numerical analysis | Mining industry | Analysis
Journal Article
SIAM journal on imaging sciences, ISSN 1936-4954, 2012, Volume 5, Issue 1, pp. 244 - 310
Journal Article
Annals of global analysis and geometry, ISSN 1572-9060, 2018, Volume 54, Issue 2, pp. 173 - 185
...) -spaces with Boeckx invariant $$I \le -1$$ I≤-1 . In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly... 
(\kappa , \mu )$$ ( κ , μ ) -space | 53C40 | Mathematical Physics | Totally umbilical | Mathematics | 53C15 | 53C25 | Geometry | Legendrian submanifold | Totally geodesic | Analysis | Global Analysis and Analysis on Manifolds | Differential Geometry | (κ, μ) -space | MATHEMATICS | (kappa, mu)-space | Resveratrol | Manifolds (mathematics) | Mathematics - Differential Geometry
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 02/2016, Volume 27, Issue 2, p. 1650002
We define a Larotonda space as a quotient space = / ℬ of the unitary groups of C ∗ -algebras 1 ∈ ℬ... 
geodesic | Finsler metric | unitary group of a C-algebra | homogeneous space | MATHEMATICS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2014, Volume 366, Issue 5, pp. 2699 - 2718
ää The space of geodesics L^{\pm }(\mathbb{S}^{n+1}_{p,1}) \mathbb{S}^{n+1}_{p,1} (\mathbb{J},\mathbb{G}) L^{\pm }(\mathbb{S}^{n+1}_{p,1}) (\mathbb{J}',\mathbb... 
Geometry | Tensors | Mathematical theorems | Hypersurfaces | Geodesy | Scalars | Mathematical vectors | Mathematical congruence | Lagrangian function | Curvature | MATHEMATICS | ORIENTED GEODESICS | LINES | SURFACES | GEOMETRY
Journal Article