Potential Theory on Sierpiński Carpets

With Applications to Uniformization

Dimitrios Ntalampekos (Autor)

Buch | Softcover

X, 186 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-50804-3 (ISBN)

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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. 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.

Dimitrios Ntalampekos is a Milnor Lecturer at Stony Brook University, working in the field of analysis on metric spaces. He completed his PhD degree at the University of California, Los Angeles under the supervision of Mario Bonk. He holds a MS in Mathematics from the same university, and pursued his undergraduate studies at the Aristotle University of Thessaloniki.

- Introduction. - Harmonic Functions on Sierpinski Carpets. - Uniformization of Sierpinski Carpets by Square Carpets.

Erscheinungsdatum	03.09.2020
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	X, 186 p. 10 illus., 4 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	308 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Harmonic Functions • Potential Theory • QuasiConformal • Quasisymmetry • Sierpinski carpets • Sierpiński Carpets • Sobolev spaces • Square Carpets • uniformization
ISBN-10	3-030-50804-8 / 3030508048
ISBN-13	978-3-030-50804-3 / 9783030508043
Zustand	Neuware