Publication

Algèbres de Royden et homéomorphismes à p-dilatation bornée entre espaces métriques mesurés

Khaled Gafaiti
2001
Theses

Abstract

The goal of this thesis is to introduce the notions of Royden algebra and mapping with bounded p-dilation between metric measure spaces. In particular, we give sufficient conditions for a metric measure space to be characterized, up to bilipschitz equivalence, by its Royden algebra. We also study sufficient conditions for mapping with bounded p-dilation between metric measure spaces to be a quasi-isometry or to be a lipschitiz map. Our results are obtained in the framework of the theory of axiomatic Sobolev spaces on metric measure spaces and are thus of a very general nature. However, we show that the application of these results to the particular case of nilpotent Lie groups with a Hörmander system gives new concrete information on the geometry of these groups.

Official source

https://infoscience.epfl.ch/entities/publication/448e02b0-b93a-4e77-872c-33bad2290064

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Khaled Gafaiti
2001
Theses

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/448e02b0-b93a-4e77-872c-33bad2290064

About this result

Related concepts (32)

Metric space

In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane.

Pseudometric space

In mathematics, a pseudometric space is a generalization of a metric space in which the distance between two distinct points can be zero. Pseudometric spaces were introduced by Đuro Kurepa in 1934. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this analogy the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is called a gauge space.

Geometry

Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

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