Potential Theory on Sierpiński Carpets
With Applications to Uniformization
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Beschreibung
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.
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.
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
Autor*in
Dimitrios Ntalampekos
Themen in »Potential Theory on Sierpiński Carpets«
Harmonic Functions Quasiconformal Quasisymmetry Sierpiński Carpets Square Carpets Sobolev Spaces Uniformization