Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets

José M. Mazón, Julio Daniel Rossi, J. Julián Toledo

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English

Springer Nature Switzerland AG
29 April 2019

Differential calculus & equations; Integral calculus & equations; Calculus of variations; Optimisation

Series: Frontiers in Mathematics

This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them.

These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained.

Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.

By: José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2019 ed.
Dimensions: Height: 240mm, Width: 168mm,
Weight: 454g
ISBN: 9783030062422
ISBN 10: 3030062422
Series: Frontiers in Mathematics
Pages: 123
Publication Date: 29 April 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Nonlocal Perimeter.- Nonlocal Isoperimetric Inequality.- Nonlocal Minimal Surfaces and Nonlocal Curvature.- Nonlocal Operators.- Nonlocal Cheeger and Calibrable Sets.- Nonlocal Heat Content.- A Nonlocal Mean Curvature Flow.- Bibliography.- Index.