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  • Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents.
  • Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents. (en)
Title
  • Scaling exponents of curvature measures
  • Scaling exponents of curvature measures (en)
skos:prefLabel
  • Scaling exponents of curvature measures
  • Scaling exponents of curvature measures (en)
skos:notation
  • RIV/00216208:11320/14:10286403!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita
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  • I, P(GCP201/10/J039)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 43853
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/14:10286403
http://linked.open...riv/jazykVysledku
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  • locally flat; self-similar set; scaling exponent; fractal curvature; S-dimension; Minkowski dimension; curvature-direction measure; curvature measure; Parallel set (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV
  • [7633472C0075]
http://linked.open...i/riv/nazevZdroje
  • Journal of fractal geometry
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2014/1
http://linked.open...iv/tvurceVysledku
  • Pokorný, Dušan
  • Winter, Steffen
issn
  • 2308-1309
number of pages
http://bibframe.org/vocab/doi
  • 10.4171/JFG/5
http://localhost/t...ganizacniJednotka
  • 11320
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