Caratheodory's and Kobayashi's metrics on Teichmueller space
Frederick P. Gardiner
TL;DR
This paper investigates the relationship between Caratheodory's and Kobayashi's metrics on Teichmueller spaces, showing they are never equal in certain tangent directions defined by separating cylindrical differentials.
Contribution
It demonstrates that these two intrinsic metrics differ in all directions associated with separating cylindrical differentials on Teichmueller spaces of dimension two or more.
Findings
Caratheodory's and Kobayashi's metrics are not equal in these spaces.
The difference is specifically in directions defined by separating cylindrical differentials.
This provides insight into the geometric structure of Teichmueller spaces.
Abstract
Caratheodory's and Kobayashi's metrics on Teichmueller spaces of dimension two or more are never equal in the direction of any tangent vector defined by a separating cylindrical differential
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Taxonomy
TopicsGeometric and Algebraic Topology · Holomorphic and Operator Theory · Geometric Analysis and Curvature Flows