Analysis of and on Uniformly Rectifiable Sets - Couverture rigide

American Mathematical Society

 
9780821815373: Analysis of and on Uniformly Rectifiable Sets

Synopsis

The notion of uniform rectifiability of sets (in a Euclidean space), which emerged only recently, can be wed in several different ways. It can be wed 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 ysis; 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, the book also poses many open problems, some of which are quite basic.

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