Results 21 to 30 of about 2,961 (99)

Topological barriers for locally homeomorphic quasiregular mappings in 3-space

, 2017
We construct a new type of locally homeomorphic quasiregular mappings in the 3-sphere and discuss their relation to the M.A.Lavrentiev problem, the Zorich map with an essential singularity at infinity, the Fatou's problem and a quasiregular analogue of ...
Apanasov, Boris N.
core   +1 more source

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

Entire functions with Cantor bouquet Julia sets

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract A hyperbolic transcendental entire function with connected Fatou set is said to be of disjoint type. It is known that the Julia set of a disjoint‐type function of finite order is a Cantor bouquet; in particular, it is a collection of arcs (‘hairs'), each connecting a finite endpoint to infinity.
Leticia Pardo‐Simón, Lasse Rempe
wiley   +1 more source

On the boundary of an immediate attracting basin of a hyperbolic entire function

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract Let f$f$ be a transcendental entire function of finite order which has an attracting periodic point z0$z_0$ of period at least 2. Suppose that the set of singularities of the inverse of f$f$ is finite and contained in the component U$U$ of the Fatou set that contains z0$z_0$. Under an additional hypothesis, we show that the intersection of ∂U$\
Walter Bergweiler, Jie Ding
wiley   +1 more source

Modular Equations and Distortion Functions

, 2007
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings.
B.C. Berndt, B.C. Berndt, C.-Q. He, D. Partyka, D. Partyka, E.T. Whittaker, F. Bowman, G. D. Anderson, G. Martin, G.D. Anderson, G.D. Anderson, G.D. Anderson, G.D. Anderson, G.D. Anderson, J. Hempel, J. Hersch, J. Jenkins, J. Väisälä, J. Väisälä, J. Zaja̧c, J.M. Borwein, M. Vuorinen, M. Vuorinen, M. Vuorinen, M.K. Vamanamurthy, O. Lehto, O. Lehto, P. Seittenranta, P. Tukia, P.F. Byrd, P.P. Belinskii, S. Agard, S. Agard, S. Yamashita, S. Zhang, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, W.K. Hayman, W.K. Hayman, Z. Li   +45 more
core   +2 more sources

Lipschitz decompositions of domains with bilaterally flat boundaries

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We study classes of domains in Rd+1,d⩾2$\mathbb {R}^{d+1},\ d \geqslant 2$ with sufficiently flat boundaries that admit a decomposition or covering of bounded overlap by Lipschitz graph domains with controlled total surface area. This study is motivated by the following result proved by Peter Jones as a piece of his proof of the Analyst's ...
Jared Krandel
wiley   +1 more source

Quasisymmetric distortion spectrum

, 2009
We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension.
Prause, István, Smirnov, Stanislav
core   +2 more sources

Extremal plane quasiconformal mappings with given boundary values

, 1973
Publisher Summary This chapter discusses the quasiconformal self mappings f = f x of the unit disc E: |z| x denotes the complex dilatation of the mapping f . By continuation, f induces a homeomorphism of the boundary ∂E onto itself.
E. Reich, K. Strebel
semanticscholar   +1 more source

GPU‐Accelerated Optimization of Discrete Ricci Flow for High‐Resolution Triangular Meshes

IET Image Processing, Volume 19, Issue 1, January/December 2025.
Discrete Ricci flow is a valuable technique for surface parameterization via target curvatures but suffers from high computational costs. This paper overcomes this bottleneck by proposing a GPU‐accelerated framework that reformulates the iterative process into parallel matrix computations. Experiments confirm the GPU implementation achieves significant
Zhiheng Wei, Kun Qian, Yinghua Li, Siyuan Li, Jialing Zhang, Junrong Song, Ming Yang, Ming Ni   +7 more
wiley   +1 more source

Radii of covering disks for locally univalent harmonic mappings

, 2016
For a univalent smooth mapping $f$ of the unit disk $\ID$ of complex plane onto the manifold $f(\ID)$, let $d_f(z_0)$ be the radius of the largest univalent disk on the manifold $f(\ID)$ centered at $f(z_0)$ ($|z_0|
Graf, Sergey Yu., Ponnusamy, Saminathan, Starkov, Victor V.   +2 more
core   +1 more source