Stephen Semmes (2001)
Publicacions Matemàtiques
Similarity:
In this paper, we give an overview of some topics involving behavior of homeomorphisms and ways in which real analysis can arise in geometric settings.
Baisheng Yan (1996)
Annales de l'I.H.P. Analyse non linéaire
Similarity:
Stephen Semmes (1996)
Revista Matemática Iberoamericana
Similarity:
In this paper we resolve in the affirmative a question of Heinonen on the absolute continuity of quasisymmetric mappings defined on subsets of Euclidean spaces. The main ingredients in the proof are extension results for quasisymmetric mappings and metric doubling measures.
Stephen Semmes (1996)
Revista Matemática Iberoamericana
Similarity:
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...
Guy David, Stephen Semmes (2000)
Publicacions Matemàtiques
Similarity:
The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat...
Guoen Hu (2003)
Publicacions Matemàtiques
Similarity:
Some boundedness results are established for sublinear operators on the homogeneous Herz spaces. As applications, some new theorems about the boundedness on homogeneous Herz spaces for commutators of singular integral operators are obtained.
Stephen Semmes (1999)
Publicacions Matemàtiques
Similarity:
When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small ("snowflake") deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat...
Mario Bonk, Juha Heinonen (2004)
Publications Mathématiques de l'IHÉS
Similarity:
We give an example of a -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in-space has Hausdorff dimension quantitatively bounded away from . By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.