Overview
- Reflects the most recent developments in the field
- The exposition is entirely self-contained
- Provides detailed proofs preceded by outlines for the convenience of the reader
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2268)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (3 chapters)
Keywords
About this book
This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpiński carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this theory is utilized to prove a uniformization result for Sierpiński carpets. This book is intended for researchers in the fields of potential theory, quasiconformal geometry, geometric group theory, complex dynamics, geometric function theory and PDEs.
Authors and Affiliations
About the author
Dimitrios Ntalampekos is a Milnor Lecturer at Stony Brook University, working in the field of analysis on metric spaces. He completed his PhD degree at the University of California, Los Angeles under the supervision of Mario Bonk. He holds a MS in Mathematics from the same university, and pursued his undergraduate studies at the Aristotle University of Thessaloniki.
Bibliographic Information
Book Title: Potential Theory on Sierpiński Carpets
Book Subtitle: With Applications to Uniformization
Authors: Dimitrios Ntalampekos
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-50805-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-50804-3Published: 02 September 2020
eBook ISBN: 978-3-030-50805-0Published: 01 September 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 186
Number of Illustrations: 6 b/w illustrations, 4 illustrations in colour
Topics: Functions of a Complex Variable, Potential Theory, Functional Analysis, Measure and Integration, Analysis