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

Auteur: David, Guy (1957-) - AuteurCo-auteur: Semmes, Stephen (1962-) - AuteurType de document: MonographieCollection: Mathematical surveys and monographs ; 38Langue: anglaisPays: Etats UnisÉditeur: Providence : American Mathematical Society, 1993Description: 1 vol. (XII-356 p.) : ill. ; 26 cm ISBN: 0821815377 ; rel. Résumé: The notion of uniform rectifiability of sets (in a Euclidean space), which emerged only recently, can be viewed in several different ways. It can be viewed as a quantitative and scale-invariant substitute for the classical notion of rectifiability; as the answer (sometimes only conjecturally) to certain geometric questions in complex and harmonic analysis; as a condition which ensures the parametrizability of a given set, with estimates, but with some holes and self-intersections allowed; and as an achievable baseline for information about the structure of a set. This book is about understanding uniform rectifiability of a given set in terms of the approximate behavior of the set at most locations and scales. In addition to being the only general reference available on uniform rectifiability, this book also poses many open problems, some of which are quite basic. (source : AMS).Bibliographie: Bibliogr. (p. 345-347). index. Sujets MSC: 42B20 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.)
49Q15 Calculus of variations and optimal control; optimization -- Manifolds -- Geometric measure and integration theory, integral and normal currents
28A75 Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory
30G35 Functions of a complex variable -- Generalized function theory -- Functions of hypercomplex variables and generalized variables
30C65 Functions of a complex variable -- Geometric function theory -- Quasiconformal mappings in Rn, other generalizations
En-ligne: Zentralblatt | MathScinet | AMS
Location Call Number Status Date Due
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Bibliogr. (p. 345-347). index

The notion of uniform rectifiability of sets (in a Euclidean space), which emerged only recently, can be viewed in several different ways. It can be viewed as a quantitative and scale-invariant substitute for the classical notion of rectifiability; as the answer (sometimes only conjecturally) to certain geometric questions in complex and harmonic analysis; as a condition which ensures the parametrizability of a given set, with estimates, but with some holes and self-intersections allowed; and as an achievable baseline for information about the structure of a set. This book is about understanding uniform rectifiability of a given set in terms of the approximate behavior of the set at most locations and scales. In addition to being the only general reference available on uniform rectifiability, this book also poses many open problems, some of which are quite basic. (source : AMS)

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