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  • For a large class of self-similar sets F in R-d, analogues of the higher-order mean curvatures of differentiable sub-manifolds are introduced-in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated fractal curvature measures, which are all multiples of the corresponding Hausdorff measures on F, due to its self-similarity. This local approach based on ergodic theory for an associated dynamical system enables us to extend former total curvature results.
  • For a large class of self-similar sets F in R-d, analogues of the higher-order mean curvatures of differentiable sub-manifolds are introduced-in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated fractal curvature measures, which are all multiples of the corresponding Hausdorff measures on F, due to its self-similarity. This local approach based on ergodic theory for an associated dynamical system enables us to extend former total curvature results. (en)
Title
  • Curvature Densities of Self-Similar Sets
  • Curvature Densities of Self-Similar Sets (en)
skos:prefLabel
  • Curvature Densities of Self-Similar Sets
  • Curvature Densities of Self-Similar Sets (en)
skos:notation
  • RIV/00216208:11320/12:10140181!RIV14-GA0-11320___
http://linked.open...avai/predkladatel
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  • P(GCP201/10/J039)
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  • 4
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  • 129299
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  • RIV/00216208:11320/12:10140181
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  • dynamical system; fractal curvatures; self-similar sets (en)
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  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [F4658E3B3E0C]
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  • Indiana University Mathematics Journal
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  • 61
http://linked.open...iv/tvurceVysledku
  • Rataj, Jan
  • Zaehle, Martina
http://linked.open...ain/vavai/riv/wos
  • 000323187700003
issn
  • 0022-2518
number of pages
http://bibframe.org/vocab/doi
  • 10.1512/iumj.2012.61.4681
http://localhost/t...ganizacniJednotka
  • 11320
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