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

Data: 2004
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Hausdorff dimension ; Quasiminimal sets ; Restricted sets ; Atness
Publicat a: Publicacions matematiques, V. 48 N. 1 (2004) , p. 187-225, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_48104_09

40 p, 280.7 KB

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