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Harmonic maps for Hitchin representations

Li, Qiongling (2019) Harmonic maps for Hitchin representations. Geometric and Functional Analysis, 29 (2). pp. 539-560. ISSN 1016-443X. https://resolver.caltech.edu/CaltechAUTHORS:20190409-103324671

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Abstract

Let (S,g_0) be a hyperbolic surface, ρ be a Hitchin representation for PSL(n,R), and f be the unique ρ-equivariant harmonic map from (S,g_0) to the corresponding symmetric space. We show its energy density satisfies e(f) ≥ 1 and equality holds at one point only if e(f) ≡ 1 and ρ is the base n-Fuchsian representation of (S,g_0). In particular, we show given a Hitchin representation ρ for PSL(n,R), every ρ-equivariant minimal immersion f from the hyperbolic plane H^2 into the corresponding symmetric space X is distance-increasing, i.e. f∗gX ≥ gH^2. Equality holds at one point only if it holds everywhere and ρ is an n-Fuchsian representation.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00039-019-00491-7DOIArticle
https://arxiv.org/abs/1806.06884arXivDiscussion Paper
Additional Information:© 2019 Springer Nature Switzerland AG. First Online: 09 April 2019. The author wants to thank the referee for many useful comments and corrections. The author is supported in part by the center of excellence Grant ‘Center for Quantum Geometry of Moduli Spaces’ from the Danish National Research Foundation (DNRF95). The author acknowledges support from U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). The author acknowledges support from Nankai Zhide Foundation.
Funders:
Funding AgencyGrant Number
Danish National Research FoundationDNRF95
NSFDMS-1107452
NSFDMS-1107263
NSFDMS-1107367
Nankai Zhide FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20190409-103324671
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190409-103324671
Official Citation:Li, Q. Geom. Funct. Anal. (2019) 29: 539. https://doi.org/10.1007/s00039-019-00491-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94582
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Apr 2019 18:00
Last Modified:03 Oct 2019 21:05

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