Zobrazeno 1 - 10
of 331
pro vyhledávání: '"30l10"'
It is a major problem in analysis on metric spaces to understand when a metric space is quasisymmetric to a space with strong analytic structure, a so-called Loewner space. A conjecture of Kleiner, recently disproven by Anttila and the second author,
Externí odkaz:
http://arxiv.org/abs/2408.17279
Autor:
Ntalampekos, Dimitrios
We characterize conformally removable sets in the plane with the aid of the recent developments in the theory of metric surfaces. We prove that a compact set in the plane is $S$-removable if and only if there exists a quasiconformal map from the plan
Externí odkaz:
http://arxiv.org/abs/2408.17174
We introduce iterated graph systems which yield fractal spaces through a projective sequence of self-similar graphs. Our construction yields new examples of self-similar fractals, such as the pentagonal Sierpi\'nski carpet and a pillow-space, and it
Externí odkaz:
http://arxiv.org/abs/2408.15692
Autor:
Rajala, Kai
Classical extremal length (or conformal modulus) is a conformal invariant involving families of paths on the Riemann sphere. In ``Extremal length and functional completion'', Fuglede initiated an abstract theory of extremal length which has since bee
Externí odkaz:
http://arxiv.org/abs/2408.12027
Autor:
Allu, Vasudevarao, Jose, Alan P
For any intrinsic Gromov hyperbolic space we establish a Gehring-Hayman type theorem for conformally deformed spaces. As an application, we prove that any complete intrinsic hyperbolic space with atleast two points in the Gromov boundary can be unifo
Externí odkaz:
http://arxiv.org/abs/2408.01412
We consider the affine-additive group as a metric measure space with a canonical left-invariant measure and a left-invariant sub-Riemannian metric. We prove that this metric measure space is locally 4-Ahlfors regular and it is hyperbolic, meaning tha
Externí odkaz:
http://arxiv.org/abs/2407.04635
The combinatorial Loewner property was introduced by Bourdon and Kleiner as a quasisymmetrically invariant substitute for the Loewner property for general fractals and boundaries of hyperbolic groups. While the Loewner property is somewhat restrictiv
Externí odkaz:
http://arxiv.org/abs/2406.08062
Autor:
Allu, Vasudevarao, Pandey, Abhishek
In this paper, we introduce the concept of quasihyperbolically visible spaces. As a tool, we study the connection between the Gromov boundary and the metric boundary.
Comment: 12 pages. Comments are welcome. arXiv admin note: text overlap with a
Comment: 12 pages. Comments are welcome. arXiv admin note: text overlap with a
Externí odkaz:
http://arxiv.org/abs/2405.10273
Autor:
Meier, Damaris, Rajala, Kai
We explore the interplay between different definitions of distortion for mappings $f\colon X\to \mathbb{R}^2$, where $X$ is any metric surface, meaning that $X$ is homeomorphic to a domain in $\mathbb{R}^2$ and has locally finite 2-dimensional Hausdo
Externí odkaz:
http://arxiv.org/abs/2405.07476
Autor:
Heikkilä, Susanna
Let $N$ be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular $\omega$-curve $\mathbb{R}^n \to N$ with infinite energy. We prove that, if the de Rham class of $\omega$ is non-zero and belongs to a so-called K\"unneth i
Externí odkaz:
http://arxiv.org/abs/2312.04347