Abstract
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We define a new conformal invariant on complete noncompact hyperbolic
surfaces that can be conformally compactified to bounded domains in
. We
study and compute this invariant up to doubly connected surfaces. Our results give a
new geometric criterion for choosing canonical representations of bounded domains in
.
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Keywords
Liouville's equation, global coefficient, conformal
geometry
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Mathematical Subject Classification
Primary: 53A05, 53C18
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Milestones
Received: 2 October 2023
Accepted: 30 November 2024
Published: 30 December 2024
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