Hyperbolization of the limit sets of some geometric constructions | Zendy

Zhanqi Zhang | Zendy; Yingqing Xiao | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Hyperbolization 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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research