Título inglés | Checkerboards, Lipschitz functions and uniform rectifiability. |
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Título español | Tableros de juego, funciones de Lipschitz y rectificabilidad uniforme. |
Autor/es | Jones, Peter W. ; Katz, Nets Hawk ; Vargas, Ana |
Organización | Dep. Math. Yale Univ., New Haven (Connecticut), Estados Unidos;Dep. Math. Univ. Edinburgh, Edimburgo, Reino Unido;Dep. Mat. Univ. Autón. Madrid, Madrid, España |
Revista | 0213-2230 |
Publicación | 1997, 13 (1): 189-210, 11 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof. Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) Ì Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε. 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. |
Clasificación UNESCO | 121009 |
Palabras clave español | Espacios lineales topológicos ; Función lipschitziana ; Curvas alabeadas ; Grafos ; Rectificación |
Código MathReviews | MR1462331 |
Código Z-Math | Zbl 0908.49029 |
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