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Analysis of and on Uniformly Rectifiable Sets
About this Title
Guy David, University of Paris-Sud, Orsay, France and Stephen Semmes, Rice University, Houston, TX
Publication: Mathematical Surveys and Monographs
Publication Year:
1993; Volume 38
ISBNs: 978-0-8218-1537-3 (print); 978-1-4704-1265-4 (online)
DOI: https://doi.org/10.1090/surv/038
MathSciNet review: MR1251061
MSC: Primary 28A75; Secondary 30C65, 30E20, 42B20, 42B25
Table of Contents
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Front/Back Matter
Part I. Background information and the statements of the main results
- 1. Reviews of various topics
- 2. A summary of the main results
- 3. Dyadic cubes and corona decompositions
Part II. New geometrical conditions related to uniform rectifiability
- 1. One-dimensional sets
- 2. The bilateral weak geometric lemma and its variants
- 3. The WHIP and related conditions
- 4. Other conditions in the codimension 1 case
Part III. Applications
- 1. Uniform rectifiability and singular integral operators
- 2. Uniform rectifiability and square function estimates for the Cauchy kernel
- 3. Square function estimates and uniform rectifiability in higher dimensions
- 4. Approximating Lipschitz functions by affine functions
- 5. The weak constant density condition
Part IV. Direct arguments for some stability results