Thurston's asymmetric metric on Margulis spacetimes
Krishnendu Gongopadhyay, Neelanjan Mondal
TL;DR
This paper extends Thurston's asymmetric metric and Finsler norm from Teichmüller space to Margulis spacetimes, revealing convexity properties in this new setting.
Contribution
It introduces a novel extension of Thurston's metric and norm to Margulis spacetimes, expanding their applicability.
Findings
Extended Thurston's asymmetric metric to Margulis spacetimes
Proved convexity properties of the extended metric and norm
Established foundational properties for future research in this area
Abstract
In this article, we extend Thurston's asymmetric metric and the associated Finsler norm, originally defined for Teichm\"uller space, to the setting of Margulis spacetimes. We also establish several convexity properties of both the asymmetric metric and the corresponding Finsler norm.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Analytic and geometric function theory · Geometric Analysis and Curvature Flows