Isoperimetric Sandwiches and Approximation by Analytic and Harmonic Functions (Chapman & Hall/CRC Monographs and Research Notes in Mathemat)
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Publication Date: September 30th, 2024
Publisher:
CRC Press
ISBN:
9781498756365
Pages:
304
Description
The book focuses on a number of results and open problems dealing with a wide variety of isoperimetric inequalities., this approach can be characterized by a recently coined term "sandwiches". A certain quantity is introduced, usually as a degree of approximation to a given simple function, e.g., z*, -x- 2, by either analytic or harmonic functions in some norm. Then, the estimates from below and above of the approximate distance are obtained in terms of simple geometric characteristics of the set, e.g., area, perimeter, capacity, etc. The resulting "sandwich" yields the isoperimetric inequality.
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