Additive continuity of the renormalized volume under geometric limits

2017/08/14 by Franco Vargas Pallete, Pallete, Franco Vargas · 1 citation
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.1708.04009

openalex publication_date 2017/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the appropriate notion of limit. This result generalizes previous work in the subject.

Citations

• On the Renormalized Volume of Hyperbolic 3-Manifolds
• Continuity of the renormalized volume under geometric limits

Cited by

• Adapted Renormalized Volume for Hyperbolic 3-Manifolds with Compressible Boundary

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