Corona Decompositions for Parabolic Uniformly Rectifiable Sets

We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows us to conclude that if Σ ⊂ R n + 1 is parabolic Ahlfors-David regular, then the following statements are equivalent. Σ is...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 33; no. 3
Main Authors Bortz, S., Hoffman, J., Hofmann, S., Luna-Garcia, J. L., Nyström, K.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2023
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Convex and Discrete Geometry
Decomposition
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Graphs
Mathematics
Mathematics and Statistics
Parabolic uniform rectifiability
28A75
30L99
43A85
Corona decompositions
Geometric measure theory
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Summary:We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows us to conclude that if Σ ⊂ R n + 1 is parabolic Ahlfors-David regular, then the following statements are equivalent. Σ is parabolic uniformly rectifiable. Σ admits a corona decomposition with respect to regular Lip(1,1/2) graphs. Σ admits a bilateral corona decomposition with respect to regular Lip(1,1/2) graphs. Σ is big pieces squared of regular Lip(1,1/2) graphs.
ISSN:1050-6926
1559-002X
1559-002X
DOI:10.1007/s12220-022-01176-8