Quasiregular mappings and the p-Laplace operator
نویسندگان
چکیده
We describe the role of p-harmonic functions in the theory of quasiregular mappings.
منابع مشابه
Examples of Uniformly Quasiregular Mappings
In this paper we construct examples of uniformly quasiregular (uqr) mappings. These provide counterexamples for a rigidity conjecture in quasiregular dynamics. It states that a closed manifold of dimension at least three, which admits a branched uqr mapping, is quasiconformally equivalent to an ordinary sphere Sn. 1. Statements and results In this paper we construct examples of a certain type o...
متن کاملNonlinear Picone identities to Pseudo $p$-Laplace operator and applications
In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...
متن کاملThe Martingale Structure of the Beurling-ahlfors Transform
The Beurling-Ahlfors operator reveals a rich structure through its representation as a martingale transform. Using elementary linear algebra and martingale inequalities, we obtain new information on this operator. In particular, Essén-type inequalities are proved for the complex Beurling-Ahlfors operator and its generalization to higher dimensions. Moreover, a new estimate of their norms is obt...
متن کاملMappings of Bounded Mean Distortion and Cohomology
T 2 are the only closed Riemann surfaces admitting nonconstant conformal mappings from the complex plane. The same rigidity is present in higher dimensions; closed manifolds admitting conformal mappings from Rn are quotients of Sn and Tn, see e.g. [2, Prop. 1.4]. However, if distortion is allowed, simple examples show that the spaces Sk1 × Sk2 × · · · × Skl (k1 + · · ·+ kl = n) receive nonconst...
متن کاملUniformly Quasiregular Maps with Toroidal Julia Sets
The iterates of a uniformly quasiregular map acting on a Riemannian manifold are quasiregular with a uniform bound on the dilatation. There is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We construct the first examples of uniformly quasiregular mappings that have a 2-torus as the Julia set. The spaces supporting this type of mappings incl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003