Checkerboards, Lipschitz functions and uniform rectifiability

Autores: Ana Vargas Rey , Nets Hawk Katz, P. W. Jones
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 13, Nº 1, 1997, págs. 189-210
Idioma: inglés
DOI: 10.4171/rmi/219
Títulos paralelos:
- Tableros de juego, funciones de Lipschitz y rectificabilidad uniforme
Enlaces
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Resumen
- In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof.
  
  Theorem. Suppose O is a bounded open set in Rn with n > 2, and suppose that B(0,1) Ì O, Hn-1(?O) = M < 8 (depending on n and M) and a Lipschitz graph G (with constant L) such that Hn-1(G n ?O) = e.
  
  Here Hk denotes k-dimensional Hausdorff measure and B(0,1) the unit ball in Rn. By iterating our proof we obtain a slightly stronger result which allows us to cover most of the unit sphere Sn-1.