Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets (Frontiers in Mathematics)

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

Springer Nature Switzerland AG（2019/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 123 p.
• 商品コード 9783030062422

Full Description

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.

Contents

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.