Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds

2023/10/16 by Bridgeman, Martin, Bromberg, Kenneth
#30F60 #32G15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2310.10890

Abstract

We bound the derivative of complex length of a geodesic under variation of the projective structure on a closed surface in terms of the norm of the Schwarzian in a neighborhood of the geodesic. One application is to cone-manifold deformations of acylindrical hyperbolic 3-manifolds.

Related

• Flat Metrics, Cubic Differentials and Limits of Projective Holonomies
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