Characterising the big pieces of Lipschitz graphs property using projections

Henri Martikainen; Tuomas Orponen

doi:10.4171/JEMS/782

Characterising the big pieces of Lipschitz graphs property using projections

Henri Martikainen
, Tuomas Orponen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly speaking, we prove that if a large subset of an n-Ahlfors–David regular set E ? R^d has plenty of projections in L², then a large part of E is contained in a single Lipschitz graph. This is closely related to a question of G. David and S. Semmes.

Original language	English
Pages (from-to)	1055-1073
Number of pages	19
Journal	Journal of the European Mathematical Society
Volume	20
Issue number	5
DOIs	https://doi.org/10.4171/JEMS/782
State	Published - 2018

Keywords

Big pieces of sets
Lipschitz graphs
Projections
Uniform rectifiability

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10.4171/JEMS/782

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title = "Characterising the big pieces of Lipschitz graphs property using projections",

abstract = "We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly speaking, we prove that if a large subset of an n-Ahlfors–David regular set E ? Rd has plenty of projections in L2, then a large part of E is contained in a single Lipschitz graph. This is closely related to a question of G. David and S. Semmes.",

keywords = "Big pieces of sets, Lipschitz graphs, Projections, Uniform rectifiability",

author = "Henri Martikainen and Tuomas Orponen",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2018.",

year = "2018",

doi = "10.4171/JEMS/782",

language = "English",

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AU - Martikainen, Henri

AU - Orponen, Tuomas

N1 - Publisher Copyright: © European Mathematical Society 2018.

PY - 2018

Y1 - 2018

N2 - We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly speaking, we prove that if a large subset of an n-Ahlfors–David regular set E ? Rd has plenty of projections in L2, then a large part of E is contained in a single Lipschitz graph. This is closely related to a question of G. David and S. Semmes.

AB - We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly speaking, we prove that if a large subset of an n-Ahlfors–David regular set E ? Rd has plenty of projections in L2, then a large part of E is contained in a single Lipschitz graph. This is closely related to a question of G. David and S. Semmes.

KW - Big pieces of sets

KW - Lipschitz graphs

KW - Projections

KW - Uniform rectifiability

UR - https://www.scopus.com/pages/publications/85046946701

U2 - 10.4171/JEMS/782

DO - 10.4171/JEMS/782

M3 - Article

AN - SCOPUS:85046946701

SN - 1435-9855

VL - 20

SP - 1055

EP - 1073

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 5

ER -

Characterising the big pieces of Lipschitz graphs property using projections

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Keywords

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