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Hausdorff dimension of uniformly non flat sets with topology
David, Guy

Date: 2004
Abstract: Let d be an integer, and let E be a nonempty closed subset of Rn. Assume that E is locally uniformly non flat, in the sense that for x ∈ E and r > 0 small, E∩B(x, r) never stays ε0r-close to an affine d-plane. Also suppose that E satisfies locally uniformly some appropriate d-dimensional topological nondegeneracy condition, like Semmes' Condition B. Then the Hausdorff dimension of E is strictly larger than d. We see this as an application of uniform rectifiability results on Almgren quasiminimal (restricted) sets.
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió publicada
Subject: Hausdorff dimension ; Quasiminimal sets ; Restricted sets ; Atness
Published in: Publicacions matemàtiques, V. 48 N. 1 (2004) , p. 187-225, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38095
DOI: 10.5565/PUBLMAT_48104_09


40 p, 280.7 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles

 Record created 2006-03-13, last modified 2022-02-20



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