Limits of blaschke metrics

Charles Ouyang; Andrea Tamburelli

doi:10.1215/00127094-2021-0027

Limits of blaschke metrics

Charles Ouyang
, Andrea Tamburelli

Department of Mathematics

Research output: Contribution to journal › Review article › peer-review

10 Scopus citations

Abstract

We find a compactification of the SL.3;R/-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.

Original language	English
Pages (from-to)	1683-1722
Number of pages	40
Journal	Duke Mathematical Journal
Volume	170
Issue number	8
DOIs	https://doi.org/10.1215/00127094-2021-0027
State	Published - Jun 1 2021

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title = "Limits of blaschke metrics",

abstract = "We find a compactification of the SL.3;R/-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.",

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AU - Tamburelli, Andrea

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N2 - We find a compactification of the SL.3;R/-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.

AB - We find a compactification of the SL.3;R/-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.

UR - https://www.scopus.com/pages/publications/85108375423

U2 - 10.1215/00127094-2021-0027

DO - 10.1215/00127094-2021-0027

M3 - Review article

AN - SCOPUS:85108375423

SN - 0012-7094

VL - 170

SP - 1683

EP - 1722

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 8

ER -

Limits of blaschke metrics

Abstract

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