Published April 2019
| Submitted
Journal Article
Open
Harmonic maps for Hitchin representations
- Creators
- Li, Qiongling
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.
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.Attached Files
Submitted - 1806.06884.pdf
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Additional details
- Eprint ID
- 94582
- DOI
- 10.1007/s00039-019-00491-7
- Resolver ID
- CaltechAUTHORS:20190409-103324671
- DNRF95
- Danish National Research Foundation
- DMS-1107452
- NSF
- DMS-1107263
- NSF
- DMS-1107367
- NSF
- Nankai Zhide Foundation
- Created
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2019-04-09Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field