Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets. 1st ed. 2019

種類:

電子ブック

責任表示:

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

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2019

著者名:

• Mazón, José M.
• Rossi, Julio Daniel.
• Toledo, J. Julián.
• SpringerLink (Online service)

シリーズ名:

Frontiers in Mathematics ;

ISBN:

9783030062439 [3030062430]    

注記:

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.
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.

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