CIRCUMCENTER EXTENSION OF MOEBIUS MAPS TO CAT(−1) SPACES

Authors

Kingshook Biswas, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Annales De L Institut Fourier

Abstract

— Given a Moebius homeomorphism f : ∂X → ∂Y between boundaries of proper, geodesically complete CAT(−1) spaces X, Y , we describe an extension fb: X → Y of f, called the circumcenter map of f, which is constructed using circumcenters of expanding sets. The extension fb is shown to coincide with the (1, log 2)-quasi-isometric extension constructed in a previous paper of the author, and is locally 1/2-Holder continuous. When X, Y are complete, simply connected manifolds with sectional curvatures K satisfying −b² ≼ K ≼ −1 for some b ≽ 1 then the extension fb: X → Y is a (1, (1− ¹b ) log 2)-quasi-isometry, and is surjective. Circumcenter extension of Moebius maps is natural with respect to composition with isometries.

First Page

235

Last Page

255

DOI

10.5802/aif.3582

Publication Date

1-1-2024

Comments

Open Access; Gold Open Access; Green Open Access

Recommended Citation

Biswas, Kingshook, "CIRCUMCENTER EXTENSION OF MOEBIUS MAPS TO CAT(−1) SPACES" (2024). Journal Articles. 4649.
https://digitalcommons.isical.ac.in/journal-articles/4649