Uniform refinements, topological derivative and a differentiation theorem in metric spaces

2009/11/24 by Marius Buliga, Buliga, Marius
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0911.4619

Abstract

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and its bibliographic references. Here we propose another type of differentiation theorem, which does not involve measures. It is therefore different from Rademacher type theorems. Instead, this differentiation theorem (and the concept of uniformly topological derivable function) is formulated in terms of filters in topological spaces.

Citations

• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

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