Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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.