Potential Theory on Sierpinski Carpets : With Applications to Uniformization
1st ed. 2020
Book Details
Format
Paperback / Softback
Book Series
Lecture Notes in Mathematics
ISBN-10
3030508048
ISBN-13
9783030508043
Edition
1st ed. 2020
Publisher
Springer Nature Switzerland AG
Imprint
Springer Nature Switzerland AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Sep 2nd, 2020
Print length
186 Pages
Ksh 8,100.00
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This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces.
This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski 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 Sierpinski 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 Sierpinski 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.
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