Potential Theory on Sierpiński Carpets: With Applications to Uniformization

✍ Scribed by Dimitrios Ntalampekos

• Publisher: Springer International Publishing;Springer
• Year: 2020
• Tongue: English
• Leaves: 192
• Series: Lecture Notes in Mathematics 2268
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Introduction (Dimitrios Ntalampekos)....Pages 1-7
Harmonic Functions on Sierpiński Carpets (Dimitrios Ntalampekos)....Pages 9-89
Uniformization of Sierpiński Carpets by Square Carpets (Dimitrios Ntalampekos)....Pages 91-177
Back Matter ....Pages 179-186

✦ Subjects

Mathematics; Functions of a Complex Variable; Potential Theory; Functional Analysis; Measure and Integration; Analysis