Lengthening deformations of singular hyperbolic tori
classification
🧮 math.GT
keywords
deformationshyperbolicadmittinganswerbecomesclosedconedegenerates
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Let $S$ be a torus with a hyperbolic metric admitting one puncture or cone singularity. We describe which infinitesimal deformations of $S$ lengthen (or shrink) all closed geodesics. We also study how the answer degenerates when $S$ becomes Euclidean, i.e. very small.
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