Ntalampekos, Dimitrios. Potential Theory on Sierpiński Carpets : With Applications to Uniformization / [electronic resource] : / by Dimitrios Ntalampekos.. 1st ed. 2020.. X, 186 p. 10 illus., 4 illus. in color. : online resource. (Lecture Notes in Mathematics,) 2268 0075-8434 ;. - Lecture Notes in Mathematics, 2268 .

Анотація:
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.

ISBN: 9783030508050

Standard No.: 10.1007/978-3-030-50805-0 doi

Subjects--Topical Terms:
Functions of complex variables.
Potential theory (Mathematics).
Functional analysis.
Measure theory.
Mathematical analysis.
Analysis (Mathematics).
Functions of a Complex Variable.
Potential Theory.
Functional Analysis.
Measure and Integration.
Analysis.

LC Class. No.: QA331-355

Dewey Class. No.: 515.9