Analysis of and on uniformly rectifiable sets / Guy David, Stephen Semmes.

Format:

Book

Author/Creator:

David, Guy, 1957- author.

Semmes, Stephen, 1962- author.

Series:

Mathematical surveys and monographs ; no. 38.

Mathematical surveys and monographs, 0076-5376 ; volume 38

Language:

English

Subjects (All):

Geometric measure theory.

Singular integrals.

Functions of complex variables.

Physical Description:

1 online resource (370 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1993]

Language Note:

English

Summary:

The monograph is divided into four parts. The first gives background information and statements of main results, including dyadic cubes and corona decompositions. Part Two is on new geometrical conditions related to uniform rectifiability, and covers one-dimensional sets, the bilateral weak geometric lemma and its variants, the WHIP and related conditions, and other conditions in the codimension 1 case. The third part discusses applications such as uniform rectifiability and singular integral operators, and Part Four gives direct arguments for some stability results. Annotation copyright by Book News, Inc., Portland, OR

Contents:

""Table of Contents""; ""Preface""; ""Notation and Conventions""; ""Part I: Background Information and the Statements of the Main Results""; ""Chapter 1. Reviews of Various Topics""; ""1.1 Review from geometric measure theory""; ""1.2 Review of some topics concerning singular integral operators and rectifiability""; ""1.3 Review of some aspects of Littlewood-Paley theory in connection with rectifiability""; ""1.4 Various characterizations of uniform rectifiability""; ""1.5 The weak geometric lemma and its relatives""; ""Chapter 2. A Summary of the Main Results""

""2.1 The results of Part II""""2.2 Bilateral approximation from a functorial point of view""; ""2.3 The results of Part III""; ""2.4 A rapid description of Part IV""; ""Chapter 3. Dyadic Cubes and Corona Decompositions""; ""3.1 Cubes""; ""3.2 Corona decompositions""; ""3.3 Generalized corona decompositions""; ""Part II: New Geometrical Conditions Related to Uniform Rectifiability""; ""Chapter 1. One-Dimensional Sets""; ""1.1 The weak connectedness condition""; ""1.2 The weaker local symmetry condition (d = 1)""; ""1.3 Weak constant density for one-dimensional sets""

""1.4 The weak ""two points on spheres"" condition""""Chapter 2. The Bilateral Weak Geometric Lemma and its Variants""; ""2.1 Introduction; the corona method""; ""2.2 Big projections in codimension 1""; ""2.3 Big projections in the higher codimension case""; ""2.4 The local convexity condition LCV""; ""2.5 The weaker local convexity condition WLCV""; ""2.6 Weak starlikeness""; ""2.7 Some questions about variants of the LCV and the LS""; ""Chapter 3. The WHIP and Related Conditions""; ""3.1 The WHIP, the WTP, and uniform rectifiability""; ""3.2 The WHIP and weaker versions of the BWGL""

""3.3 The weak exterior convexity condition and the GWEC""""3.4 The weak-no-mugs, weak-no-boxes, and weak-no-reels conditions""; ""3.5 The proof of Theorem 3.9 (part 1)""; ""3.6 Part 2 of the proof: The stopping-time argument""; ""Chapter 4. Other Conditions in the Codimension 1 Case""; ""4.1 Introduction""; ""4.2 Labellings""; ""4.3 The derivation of Theorem 4.9 from Theorem 4.31""; ""Part III: Applications""; ""Chapter 1. Uniform Rectifiability and Singular Integral Operators""; ""1.1 Preliminaries""; ""1.2 Step one""; ""1.3 Step two""; ""1.4 An abstraction of Â3""

""Chapter 2. Uniform Rectifiability and Square Function Estimates for the Cauchy Kernel""""2.1 Some general comments about square function estimates""; ""2.2 Uniform rectifiability implies the USFE when d = 1""; ""2.3 From square function estimates to uniform rectifiability: Preliminary reductions and the plan of the proof""; ""2.4 The proof of Lemma 2.36""; ""2.5 A topological lemma""; ""2.6 The main step in the proof of Proposition 2.38""; ""2.7 The end of the proof of Proposition 2.38""; ""Chapter 3. Square Function Estimates and Uniform Rectifiability in Higher Dimensions""

""3.1 A brief review of Clifford analysis""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 345-347) and index.

Description based on print version record.

ISBN:

1-4704-1265-9