Extremal length boundary of Teichm\"uller space contains non-Busemann points
Hideki Miyachi
TL;DR
This paper demonstrates that the boundary of Teichmüller space, equipped with the Teichmüller metric, includes points that are not Busemann points, specifically in spaces of complex dimension two or higher.
Contribution
It proves the existence of non-Busemann points in the metric boundary of Teichmüller space for dimensions two and above, revealing new geometric boundary phenomena.
Findings
Non-Busemann points exist in the boundary of Teichmüller space.
This occurs when the complex dimension is at least two.
The result impacts understanding of the space's geometric structure.
Abstract
In this paper, we shall show that the metric boundary of the Teichmueller space with respect to the Teichmueller distance contains non-Busemann points when the complex dimension of the Teichmueller space is at least two.
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Taxonomy
TopicsGeometric and Algebraic Topology · Holomorphic and Operator Theory · Geometric Analysis and Curvature Flows