Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces

Labourie, François; Toulisse, Jérémy

doi:10.48550/arxiv.2010.05704

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…This result is closely related to a recent work of Labourie and Toulisse [19] on the maximal surfaces in H 2,2 . We also generalize the existence and uniqueness of bounded solutions to general cyclic Higgs bundles in a subsequent paper [23,Section 7].…”

Section: Properties Of Complete Solutionssupporting

confidence: 88%

Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces

Li,

Mochizuki

2020

Preprint

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On a Riemann surface with a holomorphic r-differential, one can naturally define a Toda equation and a cyclic Higgs bundle with a grading. A solution of the Toda equation is equivalent to a harmonic metric of the Higgs bundle for which the grading is orthogonal. Here we focus on a general non-compact Riemann surface with an r-differential which is not necessarily meromorphic at infinity. We introduce the notion of complete solution of the Toda equation, and we prove the existence and uniqueness of a complete solution by using techniques for both Toda equations and harmonic bundles. Moreover, we show some quantitative estimates of the complete solution.

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Section: Properties Of Complete Solutionssupporting

confidence: 88%

Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces

Li,

Mochizuki

2020

Preprint

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“…Finally, we recover Anosov representations as periodic cases of uniformly hyperbolic bundles. Uniformly hyperbolic bundle is the structure underlying the study of quasi-symmetric maps in [12].…”

Section: Uniformly Hyperbolic Bundles and Projectorsmentioning

confidence: 99%

“…Consequently, for any section D of F 0 , we write D = D + + D − where D ± are sections of F ± 0 according to the decomposition (12).…”

Section: 3mentioning

confidence: 99%

Simple length rigidity for Hitchin representations

Bridgeman

Canary

Labourie

2020

Advances in Mathematics

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Nous montrons qu'une représentation de Hitchin est déterminée par les rayons spectraux des images de courbes simples et non séparantes. Comme application, nous caractérisons les isométries de la function d'intersection pour les composantes de Hitchin en dimension 3, ainsi que pour les composantes auto-duales en toutes dimensions. Un outil important de notre démonstration est un résultat de transversalité sur les quadruplets positifs de drapeaux.-------We show that a Hitchin representation is determined by the spectral radii of the images of simple, non-separating closed curves. As a consequence, we classify isometries of the intersection function on Hitchin components of dimension 3 and on the self-dual Hitchin components in all dimensions. As an important tool in the proof, we establish a transversality result for positive quadruples of flags.

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Quasicircles and quasiperiodic surfaces in pseudo-hyperbolic spaces

Cited by 2 publications

References 21 publications

Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces

Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces

Simple length rigidity for Hitchin representations

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