Existence of quasiconformal maps with maximal stretching on any given countable set
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914945030946816 |
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| author | Bongers, Rosemarie Gill, James T. |
| author_facet | Bongers, Rosemarie Gill, James T. |
| contents | Quasiconformal maps are homeomorphisms with useful local distortion inequalities; infinitesimally, they map balls to ellipsoids with bounded eccentricity. This leads to a number of useful regularity properties, including quantitative Hölder continuity estimates; on the other hand, one can use the radial stretches to characterize the extremizers for Hölder continuity. In this work, given any bounded countable set in $\mathbb{R}^d$, we will construct an example of a $K$-quasiconformal map which exhibits the maximum stretching at each point of the set. This will provide an example of a quasiconformal map that exhibits the worst-case regularity on a surprisingly large set, and generalizes constructions from the planar setting into $\mathbb{R}^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_06177 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Existence of quasiconformal maps with maximal stretching on any given countable set Bongers, Rosemarie Gill, James T. Classical Analysis and ODEs Complex Variables 30C65 Quasiconformal maps are homeomorphisms with useful local distortion inequalities; infinitesimally, they map balls to ellipsoids with bounded eccentricity. This leads to a number of useful regularity properties, including quantitative Hölder continuity estimates; on the other hand, one can use the radial stretches to characterize the extremizers for Hölder continuity. In this work, given any bounded countable set in $\mathbb{R}^d$, we will construct an example of a $K$-quasiconformal map which exhibits the maximum stretching at each point of the set. This will provide an example of a quasiconformal map that exhibits the worst-case regularity on a surprisingly large set, and generalizes constructions from the planar setting into $\mathbb{R}^d$. |
| title | Existence of quasiconformal maps with maximal stretching on any given countable set |
| topic | Classical Analysis and ODEs Complex Variables 30C65 |
| url | https://arxiv.org/abs/2106.06177 |