Domination results in n-Fuchsian fibers in the moduli space of Higgs bundles release_3cmvdnc7gvcuve6we2awesqba4

by Song Dai, Qiongling Li

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In this article, we show some domination results on the Hitchin fibration, mainly focusing on the n-Fuchsian fibers. More precisely, we show the energy density of associated harmonic map of an n-Fuchsian representation dominates the ones of all other representations in the same Hitchin fiber, which implies the domination of topological invariants: translation length spectrum and entropy. As applications of the energy density domination results, we obtain the existence and uniqueness of equivariant minimal (or maximal) surfaces in certain product Riemannian (or pseudo-Riemannian) manifold. Our proof is based on establishing an algebraic inequality generalizing a GIT theorem of Ness on the nilpotent orbits to general orbits.
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Type  article
Stage   submitted
Date   2020-05-28
Version   v1
Language   en ?
arXiv  2005.13960v1
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