A horofunction counterpart to Teichm\"uller distance
Hidetoshi Masai
TL;DR
This paper extends the concept of horofunction compactification beyond distance functions and introduces a horofunction version of the Teichmüller distance, exploring its properties.
Contribution
It generalizes horofunction compactification to non-distance maps and defines a new horofunction analogue of the Teichmüller distance.
Findings
Introduces a horofunction counterpart to Teichmüller distance
Analyzes properties of the new horofunction distance
Extends horofunction compactification to broader classes of maps
Abstract
We generalize the horofunction compactification to maps that are not distance functions. As an application we define a horofunction counterpart to the Teichm\"uller distance, and discuss its properties.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals