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Quasiconformal distortion of the lower dimension and applications

  • Efstathios Konstantinos Chrontsios Garitsis
  • Jeremy T. Tyson
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Abstract

We study the distortion of the lower dimension and lower spectrum of sets under quasiconformal mappings. As an application, we verify weighted Hardy--Sobolev inequalities in Euclidean domains arising as quasiconformal images of domains with sufficiently regular boundaries. The regularity in question is phrased in terms of estimates for either the Assouad or the lower dimension of the complement. We also provide dilatation-dependent classification results for certain planar open sets.

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Cite

BibTeXRIS
BibTeX
@misc{garitsis2026quasiconformal,
  title = {{Quasiconformal distortion of the lower dimension and applications}},
  author = {Efstathios Konstantinos Chrontsios Garitsis and Jeremy T. Tyson},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05118},
  eprint = {2611.05118},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05118},
}
RIS
TY  - UNPB
TI  - Quasiconformal distortion of the lower dimension and applications
AU  - Efstathios Konstantinos Chrontsios Garitsis
AU  - Jeremy T. Tyson
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05118
UR  - https://arxiv.org/abs/2611.05118
AB  - We study the distortion of the lower dimension and lower spectrum of sets under quasiconformal mappings. As an application, we verify weighted Hardy--Sobolev inequalities in Euclidean domains arising as quasiconformal images of domains with sufficiently regular boundaries. The regularity in question is phrased in terms of estimates for either the Assouad or the lower dimension of the complement. We also provide dilatation-dependent classification results for certain planar open sets.
ER  -