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Best Lipschitz maps and Earthquakes

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arxiv 2410.08296 v1 pith:TK47T3XF submitted 2024-10-10 math.DG

Georgios Daskalopoulos , Karen Uhlenbeck This is my paper · ORCID
classification math.DG
keywords mapsalgebrabestlipschitzmeasuresvaluedearthquakestransverse
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This is the third paper in a series in which we prove Thurston's conjectural duality between best Lipschitz maps and transverse measures. In the second paper we found a special class of best Lipschitz maps between hyperbolic surfaces (infinity harmonic maps), which induce dual Lie algebra valued transverse measures with support on Thurston's canonical lamination. The present paper examines these Lie algebra valued measures in greater detail. For any measured lamination we are led to define a Lie algebra valued measure and conversely every Lie algebra valued transverse measure arrises from this process. Furthermore, we show that such measures are infinitesimal earthquakes. This construction provides a natural correspondence between best Lipschitz maps and earthquakes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Infinity-harmonic functions and inverse mean curvature flow clusters

    math.AP 2026-07 accept novelty 8.0 of 10

    Infinity-harmonic functions on planar domains are C^{1,1/3} with isolated critical points and unique quasiradial blow-ups, via a p-to-infinity duality that produces inverse mean curvature flow clusters.

  2. Maximal stretch and Lipschitz maps on Riemannian manifolds of negative curvature

    math.DG 2025-07 conditional novelty 8.0 of 10

    Closed negatively curved manifolds have a Mather set of maximally stretched orbits that is nowhere dense unless the two metrics have proportional marked length spectra, in which case it is the whole unit tangent bundle.

  3. The canonical lamination calibrated by a cohomology class

    math.DG 2024-11 conditional novelty 7.0 of 10

    Each unit costable cohomology class on a closed oriented Riemannian d-manifold (2 to 7) determines a unique largest lamination of minimal hypersurfaces calibrated by every calibration in the class, constraining the st...

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