Lindelöf-type theorems for quasiconformal and quasiregular mappings
Matti Vuorinen (1983)
Banach Center Publications
Similarity:
Matti Vuorinen (1983)
Banach Center Publications
Similarity:
Kari Astala, Mario Bonk, Juha Heinonen (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
We consider quasiconformal mappings in the upper half space of , , whose almost everywhere defined trace in has distributional differential in . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space . More generally, we consider certain positive functions defined on , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems...
Giovanni Porru (1977)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
V. Gutlyanskiĭ, O. Martio, V. Ryazanov, M. Vuorinen (1998)
Studia Mathematica
Similarity:
It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at implies the local injectivity and the asymptotic linearity of f at . Sufficient conditions for to behave asymptotically as are given. Some global injectivity results are derived.
Juha Heinonen (1996)
Revista Matemática Iberoamericana
Similarity:
In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B → D, where B is the unit 3-ball and D is a Jordan domain in R with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.
Juha Heinonen (1996)
Revista Matemática Iberoamericana
Similarity:
We use a recent theorem of Semmes to resolve some questions about the boundary absolute continuity of quasiconformal maps in space.
Mayer, Volker (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
Similarity:
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...
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.