L²-bounds for drilling short geodesics in convex co-compact hyperbolic 3-manifolds

2021/12/06 by Martin Bridgeman, Bridgeman, Martin, Kenneth Bromberg +1
Mathematics · #32G15 #32Q45 #51P05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2112.02724

openalex publication_date 2021/12/06 · openalex created_date 2021/12/31 · openalex updated_date 2026/08/01

Abstract

We give L²-bounds on the change in the complex projective structure on the boundary of conformally compact hyperbolic 3-manifold with incompressible boundary after drilling short geodesics. We show that the change is bounded by a universal constant times the square root of the length of the drilled geodesics. While L^∞-bounds of this type where obtained by the second author (2004), our bounds here do not depend on the injectivity radius of the boundary.

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