Harmonic maps for Hitchin representations

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  • Qiongling Li, California Inst. of Technology, Pasadena, Nankai University
Let (S, g0) be a hyperbolic surface, ρ be a Hitchin representation for P SL(n,R), and f be the unique ρ-equivariant harmonic map from (S, ̃ ̃g0) 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, g0). In particular, we show given a Hitchin representation
ρ for P SL(n,R), every ρ-equivariant minimal immersion f from a hyperbolic plane H 2 into the corresponding symmetric space X is distance-increasing, i.e. f ∗ (gX) ≥ gH2 . Equality holds at one point only if it holds everywhere and ρ is an n-Fuchsian representation.
Original languageEnglish
JournalGeometric and Functional Analysis
Pages (from-to)539-560
Number of pages22
Publication statusPublished - Apr 2019

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