Metric Structures for Riemannian and Non-Riemannian Spaces

By Misha Gromov. 1999

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Citations in the corpus

Federated Learning with Matched Averaging (2020, background): “We note that Gromov-Wasserstein distance (Gromov, 2007) from the optimal transport literature corresponds to a similar quadratic assignment problem.”
Computational Optimal Transport (2018, methodology): “2 Gromov–Hausdorff distance The Gromov–Hausdorff (GH) distance [Gromov, 2001] (see also [Edwards, 1975]) is a way to measure the distance between two metric spaces (X , dX ), (Y, dY) by quantifying how far they are from being isometric to each other, see Figure 10.”
Growth of Lévy trees (2005, background): “Observe that δcpct only depends on the isometry classes of the Xi’s and we can show that it defines a metric on the set of isometry classes of all pointed compact metric spaces (see [19]).”
Gromov Hyperbolicity of Riemann Surfaces (2007, unknown): “[12–14] and the references therein).”
Hyperbolic Geometry of Complex Networks (2010, background): “Table I collects these and other characteristic properties of hyperbolic geometry and juxtaposes them against the corresponding properties of Euclidean and spherical geometries.”
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004, background): “The fact that there exists ε > 0 such that all the balls of of radius ε in X embed bi-Lipschitzly in Rn follows from Rauch’s comparison theorem (see [12] and Chapter 8+ in [24]).”
New monotonicity formulas for Ricci curvature and applications. I (2011, methodology): “The Bishop-Gromov volume comparison theorem, [GLP], [G], was described above.”
Lectures on Lipschitz analysis (2005, unknown): “References to the topics advertized in this introduction include [18], [50], [17], [80], [20], [59], [16], [25], [63], [5], [67], [64], [47], [73], [62], [43].”
Model Theory with Applications to Algebra and Analysis: Model theory for metric structures (2008, methodology): “This construction is widely used in functional analysis and also arises in metric space geometry (see [19], for example).”
Eigenvalues and eigenfunctions of metric measure manifolds (2001, background): “M. Gromov, `Dimension, non-linear spectra and width', Geometric aspects of functional analysis (ed.”
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance (2001, background): “But certain parts of the metric and differential geometric apparatus persist [14], [16], [27], [44], [47], [30], [31], [50] [21].”
Geometrisation of 3-Manifolds (2010, result): “We next state the main compactness theorem, whose proof follows from [Gro99], [Pet87], [GW88].”