Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets

• Main Authors: Mazón, José M. (Author, http://id.loc.gov/vocabulary/relators/aut), Rossi, Julio Daniel (http://id.loc.gov/vocabulary/relators/aut), Toledo, J. Julián (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Frontiers in Mathematics,
• Subjects: Integral equations.; Measure theory.; Calculus of variations.; Partial differential equations.; Integral Equations.; Measure and Integration.; Calculus of Variations and Optimal Control; Optimization.; Partial Differential Equations.
• Physical Description: XVIII, 123 p. 2 illus., 1 illus. in color. online resource.
• ISBN: 9783030062439
• ISSN: 1660-8046
• DOI: 10.1007/978-3-030-06243-9

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.