@article{76f75142a2a5472b8976816f333dc2b7,
title = "The moduli spaces of equivariant minimal surfaces in RH3 and RH4 via Higgs bundles",
abstract = "In this article we introduce a definition for the moduli space of equivariant minimal immersions of the Poincar{\'e} disc into a non-compact symmetric space, where the equivariance is with respect to representations of the fundamental group of a compact Riemann surface of genus at least two. We then study this moduli space for the non-compact symmetric space RHn and show how SO(n, 1) -Higgs bundles can be used to parametrise this space, making clear how the classical invariants (induced metric and second fundamental form) figure in this picture. We use this parametrisation to provide details of the moduli spaces for RH3 and RH4, and relate their structure to the structure of the corresponding Higgs bundle moduli spaces.",
keywords = "Character variety, Higgs bundle, Minimal surface",
author = "John Loftin and Ian McIntosh",
note = "Funding Information: This research was supported by the LMS Scheme 4 Research in Pairs Grant # 41532 and U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). The first author is also grateful to the Simons Foundation for partial support under Collaboration Grant for Mathematicians 210124. Both authors are grateful to Laura Schaposnik and Steve Bradlow for informative conversations regarding orthogonal Higgs bundles. The second author is grateful to the Centre for Quantum Geometry of Moduli Spaces , University of Aarhus, for the opportunity to visit in Sept. 2016 and discuss early stages of this work with Qiongling Li. In particular, Sect. 3 below is based on observations made by Qiongling Li and Daniele Alessandrini and we are grateful for their permission to use their unpublished ideas here. Funding Information: This research was supported by the LMS Scheme 4 Research in Pairs Grant # 41532 and U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). The first author is also grateful to the Simons Foundation for partial support under Collaboration Grant for Mathematicians 210124. Both authors are grateful to Laura Schaposnik and Steve Bradlow for informative conversations regarding orthogonal Higgs bundles. The second author is grateful to the Centre for Quantum Geometry of Moduli Spaces, University of Aarhus, for the opportunity to visit in Sept. 2016 and discuss early stages of this work with Qiongling Li. In particular, Sect. 3 below is based on observations made by Qiongling Li and Daniele Alessandrini and we are grateful for their permission to use their unpublished ideas here. Publisher Copyright: {\textcopyright} 2018, The Author(s).",
year = "2019",
month = aug,
day = "1",
doi = "10.1007/s10711-018-0395-5",
language = "English (US)",
volume = "201",
pages = "325--351",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "1",
}