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 in:The Journal of geometric analysis 2023-03, Vol.33 (3), Article 96
Main Authors: Bortz, S., Hoffman, J., Hofmann, S., Luna-Garcia, J. L., Nyström, K.
Format: Article
Language:English
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
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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