TY  - BOOK
AU  - Ntalampekos,Dimitrios
ED  - SpringerLink (Online service)
TI  - Potential Theory on Sierpiński Carpets: With Applications to Uniformization 
T2  - Lecture Notes in Mathematics,
SN  - 9783030508050
AV  - QA331-355 
U1  - 515.9 23
PY  - 2020///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Functions of complex variables
KW  - Potential theory (Mathematics)
KW  - Functional analysis
KW  - Measure theory
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Functions of a Complex Variable
KW  - Potential Theory
KW  - Functional Analysis
KW  - Measure and Integration
KW  - Analysis
N2  - 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
UR  - https://doi.org/10.1007/978-3-030-50805-0
ER  -