# Checkerboards, Lipschitz functions and uniform rectifiability.

Peter W. Jones; Nets Hawk Katz; Ana Vargas

Revista Matemática Iberoamericana (1997)

- Volume: 13, Issue: 1, page 189-210
- ISSN: 0213-2230

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topJones, Peter W., Katz, Nets Hawk, and Vargas, Ana. "Checkerboards, Lipschitz functions and uniform rectifiability.." Revista Matemática Iberoamericana 13.1 (1997): 189-210. <http://eudml.org/doc/39527>.

@article{Jones1997,

abstract = {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) ⊂ 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.},

author = {Jones, Peter W., Katz, Nets Hawk, Vargas, Ana},

journal = {Revista Matemática Iberoamericana},

keywords = {Espacios lineales topológicos; Función lipschitziana; Curvas alabeadas; Grafos; Rectificación; Lipschitz graph; Hausdorff measure; rectifiability; checkerboard theorem},

language = {eng},

number = {1},

pages = {189-210},

title = {Checkerboards, Lipschitz functions and uniform rectifiability.},

url = {http://eudml.org/doc/39527},

volume = {13},

year = {1997},

}

TY - JOUR

AU - Jones, Peter W.

AU - Katz, Nets Hawk

AU - Vargas, Ana

TI - Checkerboards, Lipschitz functions and uniform rectifiability.

JO - Revista Matemática Iberoamericana

PY - 1997

VL - 13

IS - 1

SP - 189

EP - 210

AB - 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) ⊂ 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.

LA - eng

KW - Espacios lineales topológicos; Función lipschitziana; Curvas alabeadas; Grafos; Rectificación; Lipschitz graph; Hausdorff measure; rectifiability; checkerboard theorem

UR - http://eudml.org/doc/39527

ER -