The dual Bonahon-Schläfli formula

DOI10.2140/agt.2021.21.279zbMath1472.53086arXiv1808.08936OpenAlexW2888059944MaRDI QIDQ2664179

Filippo Mazzoli

Publication date: 20 April 2021

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.08936

zbMATH Keywords

hyperbolic geometryKleinian groupsSchläfli formulaconvex cocompactdual volumedual Bonahon-Schläfli formula

Mathematics Subject Classification ID

Integral geometry (53C65) General geometric structures on low-dimensional manifolds (57M50) Convex sets in (3) dimensions (including convex surfaces) (52A15) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) General topology of 3-manifolds (57K30)

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Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces ⋮ The infimum of the dual volume of convex cocompact hyperbolic 3-manifolds ⋮ The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance

Cites Work

• A symplectic map between hyperbolic and complex Teichmüller theory
• On the renormalized volume of hyperbolic 3-manifolds
• Earthquakes are analytic
• The geometry of Teichmüller space via geodesic currents
• A characterization of compact convex polyhedra in hyperbolic 3-space
• Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
• A Schläfli-type formula for convex cores of hyperbolic \(3\)-manifolds
• Variations of the boundary geometry of \(3\)-dimensional hyperbolic convex cores
• Continuity of convex hull boundaries
• Transverse Hölder distributions for geodesic laminations
• The renormalized volume and the volume of the convex core of quasifuchsian manifolds
• Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume
• The Schläfli formula in Einstein manifolds with boundary
• Geodesic laminations with transverse hölder distributions1

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