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This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman.
- Isoperimetric Inequalities and Amenability
Cite this chapter (2007). Isoperimetric Inequalities and...
- Morse Theory and Minimal Models
In Chapter 6, we introduced the notion of 2-dimensional...
- Manifolds With Bounded Ricci Curvature
Cite this chapter (2007). Manifolds with Bounded Ricci...
- Metric Structures on Families of Metric Spaces
Cite this chapter (2007). Metric Structures on Families of...
- Convergence and Concentration of Metrics and Measures
When we speak of measures μ on a metric space X, we always...
- Length Structures
In classical Riemannian geometry, one begins with a C ∞...
- Isoperimetric Inequalities and Amenability
We study metric contraction properties for metric spaces associated with left-invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub-Riemannian structures on Carnot groups satisfy …
Metric structures for Riemannian and non-Riemannian spaces. / August 28, 2018 / Distance geometry in Riemannian manifolds, Metric invariants and quantitative topology, Metric, measure, concentration and isoperimetric inequalities.
Metric Structures for Riemannian and Non-Riemannian Spaces. In classical Riemannian geometry, one begins with a C ∞ manifold X and then studies smooth, positive-definite sections g of the...
20 de abr. de 2001 · Metric Structures for Riemannian and Non-Riemannian Spaces. Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations...
Metric Structures for Riemannian and Non-Riemannian Spaces. Based on Structures Metriques des Varietes Riemanniennes Edited by J. LaFontaine and P. Pansu English Translation by Sean Michael Bates.
22 de dic. de 2006 · We prove lower bounds for energy functionals of mappings from real, complex and quaternionic projective spaces with their canonical (symmetric space) metrics to Riemannian manifolds.
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