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

Abstract

top
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.

How to cite

top

Jones, 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 &gt; 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M &lt; ∞ (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 &gt; 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M &lt; ∞ (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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.