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Mathematical Surveys and Monographs
1993; 356 pp; hardcover
List Price: US$129
Member Price: US$103.20
Order Code: SURV/38
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.
Harmonic analysts, complex analysts, mathematicians working in geometric measure theory, and mathematicians studying bilipshitz and quasiconformal mappings.
"A mixture of geometric measure theory and harmonic analysis ... a remarkable development of these researches."
-- Zentralblatt MATH
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