| 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 ; Versió publicada |
| Matèria: |
Hausdorff dimension ;
Quasiminimal sets ;
Restricted sets ;
Atness |
| Publicat a: |
Publicacions matemàtiques, V. 48 N. 1 (2004) , p. 187-225, ISSN 2014-4350 |
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