Results 41 to 50 of about 4,681 (167)
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.
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Angles and Quasiconformal Mappings† [PDF]
Proceedings of the London Mathematical Society, 1965 Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135391/1/plms0001 ...
Agard, S. B., Gehring, F. W.
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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
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Duality of Moduli and Quasiconformal Mappings in Metric Spaces
Analysis and Geometry in Metric Spaces, 2020 We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality.
Jones Rebekah, Lahti Panu
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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
Rigid circle domains with non‐removable boundaries
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We give a negative answer to the rigidity conjecture of He and Schramm by constructing a rigid circle domain Ω$\Omega$ on the Riemann sphere Ĉ$\hat{\mathbb {C}}$ with conformally non‐removable boundary. Here, rigidity means that every conformal map from Ω$\Omega$ onto another circle domain is a Möbius transformation, and non‐removability ...
Kai Rajala
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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$\
Walter Bergweiler, Jie Ding
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Semilinear equations in the plane with measurable data
Доповiдi Нацiональної академiї наук УкраїниWe study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form. The main result is given as a factorization theorem.
V.Ya. Gutlyanskiĭ +2 more
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Martin compactifications and quasiconformal mappings [PDF]
Proceedings of the American Mathematical Society, 1985 It is shown that there exists a quasiconformal mapping T T of a Riemann surface R 1 {R_1} onto another R 2 {R_2} such that T T cannot be extended to a homeomorphism of the Martin compactification
Segawa, Shigeo, Tada, Toshimasa
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Lipschitz decompositions of domains with bilaterally flat boundaries
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study classes of domains in Rd+1,d⩾2$\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
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