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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. doi:10.1007/s00039-019-00491-7.

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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.

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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.
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Danish National Research FoundationDNRF95
Nankai Zhide FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20190409-103324671
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Official Citation:Li, Q. Geom. Funct. Anal. (2019) 29: 539.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94582
Deposited By: Tony Diaz
Deposited On:09 Apr 2019 18:00
Last Modified:16 Nov 2021 17:06

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