Author: Dimitrios Ntalampekos
Publisher: Springer Nature
Published: 2020-09-01
Total Pages: 186
ISBN-13: 3030508056
DOWNLOAD EBOOKThis 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.
Book Synopsis Potential Theory on Sierpiński Carpets by : Dimitrios Ntalampekos
Download or read book Potential Theory on Sierpiński Carpets written by Dimitrios Ntalampekos and published by Springer Nature. This book was released on 2020-09-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.