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POTENTIAL METHOD AND PROJECTION THEOREMS FOR MACROSCOPIC HAUSDORFF DIMENSION

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  • Additional Information
    • Contributors:
      University of Luxembourg Luxembourg; Laboratoire Analyse et Mathématiques Appliquées (LAMA); Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel
    • Publication Information:
      HAL CCSD
      Elsevier
    • Publication Date:
      2023
    • Collection:
      Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
    • Abstract:
      International audience ; The macroscopic Hausdorff dimension Dim H (E) of a set E ⊂ R d was introduced by Barlow and Taylor to quantify a "fractal at large scales" behavior of unbounded, possibly discrete, sets E. We develop a method based on potential theory in order to estimate this dimension in R d. Then, we apply this method to obtain Marstrand-like projection theorems: given a set E ⊂ R 2 , for almost every θ ∈ [0, 2π], the projection of E on the straight line passing through 0 with angle θ has dimension equal to min(Dim H (E) , 1).
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2203.06954; hal-03606045; https://hal.science/hal-03606045; https://hal.science/hal-03606045/document; https://hal.science/hal-03606045/file/Projection-th-Daw-Seuret.pdf; ARXIV: 2203.06954
    • Online Access:
      https://hal.science/hal-03606045
      https://hal.science/hal-03606045/document
      https://hal.science/hal-03606045/file/Projection-th-Daw-Seuret.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.8D3E8032