Displaying similar documents to “Uniform rectifiability and singular sets”

On the nonexistence of bilipschitz parametrizations and geometric problems about A-weights.

Stephen Semmes (1996)

Revista Matemática Iberoamericana

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How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of R are already quite interesting. It is easy to generate geometric conditions which are necessary for bilipschitz equivalence, but it is not clear that such conditions should ever be sufficient. The main point of this paper is that the optimistic conjectures about the existence of bilipschitz parametrizations are...

Good metric spaces without good parameterizations.

Stephen Semmes (1996)

Revista Matemática Iberoamericana

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A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric parametrization by providing examples of spaces with many Eucledian-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can...

Harmonic analysis and the geometry of subsets of R.

Guy David, Stephen Semmes (1991)

Publicacions Matemàtiques

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This subject has several natural points of view, but we shall start with the one that corresponds to the following question: Is there something like Littlewood-Paley theory which is useful for analyzing the geometry of subsets of R, in much the same way that traditional Littlewood-Paley theory is good for analyzing functions and operators?

Measure-preserving quality within mappings.

Stephen Semmes (2000)

Revista Matemática Iberoamericana

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In [6], Guy David introduced some methods for finding controlled behavior in Lipschitz mappings with substantial images (in terms of measure). Under suitable conditions, David produces subsets on which the given mapping is bilipschitz, with uniform bounds for the bilipschitz constant and the size of the subset. This has applications for boundedness of singular integral operators and uniform rectifiability of sets, as in [6], [7], [11], [13]. Some special cases of David's results, concerning...