Potential theory on Sierpiński carpets : with applications to uniformization
著者
書誌事項
Potential theory on Sierpiński carpets : with applications to uniformization
（Lecture notes in mathematics, 2268）
Springer, c2020
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注記
Includes bibliographical references (p. 179-181) and index
内容説明・目次
内容説明
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.
目次
- Introduction. - Harmonic Functions on Sierpinski Carpets. - Uniformization of Sierpinski Carpets by Square Carpets.
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