Rectifiability: A Survey

Rectifiability, measures, currents, and varifolds have strong connections with other areas of analysis and geometry, such as the calculus of variations and complex and harmonic analysis. This book provides an overview of this field, including historical background, basic theory, and applications. It is ideal for researchers and graduate students looking to explore this area further.

Format: Paperback / softback
Length: 182 pages
Publication date: 12 January 2023
Publisher: Cambridge University Press

Geometric measure theory is a fundamental branch of mathematics that deals with the study of rectifiable sets, measures, currents, and varifolds. These concepts play a crucial role in understanding the geometry of spaces and their properties. Over the past four decades, there has been a remarkable surge in the connections between rectifiability and other areas of analysis and geometry. This field has deep connections with the calculus of variations and complex and harmonic analysis, leading to new insights and developments.

In this concise book, the author aims to provide a comprehensive overview of this wide and active field. The book begins by discussing the historical background of rectifiability, including its origins and early developments. It then delves into the basic theory in Euclidean and non-Euclidean settings, exploring the properties and characteristics of rectifiable sets and measures. The author also discusses the appearance of rectifiability in analysis and geometry, highlighting its significance in various areas such as partial differential equations, differential geometry, and topology.

One of the key strengths of this book is its accessibility to readers with a range of backgrounds. The author avoids complicated technical arguments and long proofs, instead presenting the topics in a clear and concise manner. Each chapter is accompanied by examples and exercises to help the reader grasp the concepts and apply them to real-world situations. Additionally, an extensive bibliography provides readers with a wealth of references to further explore the topics covered in the book.

This book is particularly valuable for researchers and graduate students who are interested in geometric measure theory. It offers a solid foundation for understanding the core concepts and provides inspiration for further research. The book's clear and concise writing style makes it easy to follow, and the extensive bibliography ensures that readers have access to the latest research in the field.

In conclusion, "Rectifiability in Geometric Measure Theory" is a must-read for anyone interested in the field of geometric measure theory. It provides a comprehensive and accessible overview of the topic, including discussions of historical background, basic theory, and applications. The book's clear writing style, extensive bibliography, and examples and exercises make it an ideal resource for researchers and graduate students alike.

Weight: 276g
Dimension: 153 x 229 x 15 (mm)
ISBN-13: 9781009288088