Length spectrum compactification of the SO0(2,3)-Hitchin component

Charles Ouyang; Andrea Tamburelli

doi:10.1016/j.aim.2023.108997

Length spectrum compactification of the SO₀(2,3)-Hitchin component

Charles Ouyang
, Andrea Tamburelli

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We find a compactification of the SO₀(2,3)-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space H^2,2. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of the induced metric along rays of quartic differentials.

Original language	English
Article number	108997
Journal	Advances in Mathematics
Volume	420
DOIs	https://doi.org/10.1016/j.aim.2023.108997
State	Published - May 1 2023

Keywords

Higgs bundles
Higher Teichmuller theory
Length spectrum
Maximal surfaces
Representations

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abstract = "We find a compactification of the SO0(2,3)-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space H2,2. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of the induced metric along rays of quartic differentials.",

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author = "Charles Ouyang and Andrea Tamburelli",

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AU - Tamburelli, Andrea

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N2 - We find a compactification of the SO0(2,3)-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space H2,2. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of the induced metric along rays of quartic differentials.

AB - We find a compactification of the SO0(2,3)-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space H2,2. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of the induced metric along rays of quartic differentials.

KW - Higgs bundles

KW - Higher Teichmuller theory

KW - Length spectrum

KW - Maximal surfaces

KW - Representations

UR - https://www.scopus.com/pages/publications/85151452195

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DO - 10.1016/j.aim.2023.108997

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SN - 0001-8708

VL - 420

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108997

ER -

Length spectrum compactification of the SO₀(2,3)-Hitchin component

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Keywords

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