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Description
  • We give an estimate for the Hausdorff gauge dimension of the boundary of a simply connected planar domain under p-integrability of the hyperbolic metric, p > 1. This estimate does not degenerate when p tends to one; for p = 1 the boundary can even have positive area. The same phenomenon is extended to general planar domains in terms of the quasihyperbolic metric. We also give an example which shows that our estimates are essentially sharp.
  • We give an estimate for the Hausdorff gauge dimension of the boundary of a simply connected planar domain under p-integrability of the hyperbolic metric, p > 1. This estimate does not degenerate when p tends to one; for p = 1 the boundary can even have positive area. The same phenomenon is extended to general planar domains in terms of the quasihyperbolic metric. We also give an example which shows that our estimates are essentially sharp. (en)
Title
  • Dimension gap under conformal mappings
  • Dimension gap under conformal mappings (en)
skos:prefLabel
  • Dimension gap under conformal mappings
  • Dimension gap under conformal mappings (en)
skos:notation
  • RIV/00216208:11320/12:10127315!RIV13-MSM-11320___
http://linked.open...avai/predkladatel
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  • I
http://linked.open...iv/cisloPeriodika
  • 3
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  • 131368
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  • RIV/00216208:11320/12:10127315
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  • Boundary behaviour; Hausdorff dimension; Conformal mapping (en)
http://linked.open.../riv/klicoveSlovo
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  • US - Spojené státy americké
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  • [6345ED77315E]
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  • Advances in Mathematics
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 230
http://linked.open...iv/tvurceVysledku
  • Hencl, Stanislav
  • Koskela, Pekka
  • Nieminen, Tomi
http://linked.open...ain/vavai/riv/wos
  • 000304386400025
issn
  • 0001-8708
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.aim.2012.03.018
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  • 11320
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