Open AccessHyperbolization of the limit sets of some geometric constructions
Author(s) -
Zhanqi Zhang,
Yingqing Xiao
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2005535z
Subject(s) - mathematics , hyperbolic space , limit set , fractal , pure mathematics , boundary (topology) , limit (mathematics) , cone (formal languages) , mathematical analysis , space (punctuation) , class (philosophy) , hyperbolic group , set (abstract data type) , isometric exercise , hyperbolic manifold , hyperbolic function , medicine , linguistics , philosophy , algorithm , artificial intelligence , computer science , programming language , physical therapy
Inspired by the construction of Sierpi?ski carpets, we introduce a new class of fractal sets. For a such fractal set K, we construct a Gromov hyperbolic space X (which is also a strongly hyperbolic space) and show that K is isometric to the Gromov hyperbolic boundary of X. Moreover, under some conditions, we show that Con(K) and X are roughly isometric, where Con(K) is the hyperbolic cone of K.