03216nam a22005775i 4500 978-3-030-50805-0 DE-He213 20200904105132.0 cr nn 008mamaa 200901s2020 gw | s |||| 0|eng d 9783030508050 978-3-030-50805-0 10.1007/978-3-030-50805-0 doi QA331-355 PBKD bicssc MAT034000 bisacsh PBKD thema 515.9 23 Ntalampekos, Dimitrios. author. aut http://id.loc.gov/vocabulary/relators/aut Potential Theory on Sierpiński Carpets [electronic resource] : With Applications to Uniformization / by Dimitrios Ntalampekos. 1st ed. 2020. Cham : Springer International Publishing : Imprint: Springer, 2020. X, 186 p. 10 illus., 4 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 0075-8434 ; 2268 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. Functions of complex variables. Potential theory (Mathematics). Functional analysis. Measure theory. Mathematical analysis. Analysis (Mathematics). Functions of a Complex Variable. https://scigraph.springernature.com/ontologies/product-market-codes/M12074 Potential Theory. https://scigraph.springernature.com/ontologies/product-market-codes/M12163 Functional Analysis. https://scigraph.springernature.com/ontologies/product-market-codes/M12066 Measure and Integration. https://scigraph.springernature.com/ontologies/product-market-codes/M12120 Analysis. https://scigraph.springernature.com/ontologies/product-market-codes/M12007 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783030508043 Printed edition: 9783030508067 Lecture Notes in Mathematics, 0075-8434 ; 2268 https://doi.org/10.1007/978-3-030-50805-0 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 461362 461362