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- https://arxiv.org/pdf/1806.06884.pdf
Accepted manuscript

- https://doi.org/10.1007/s00039-019-00491-7
Final published version

- 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.

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 language | English |
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Journal | Geometric and Functional Analysis |

Volume | 29 |

Issue | 2 |

Pages (from-to) | 539-560 |

Number of pages | 22 |

ISSN | 1016-443X |

DOIs | |

Publication status | Published - Apr 2019 |

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