Strict plurisubharmonicity of the energy on Teichm "uller space\n associated to Hitchin representations

2020/11/08 by Ivo Slegers, Slegers, Ivo
Mathematics · #32G15 #58E20 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2011.03936

openalex publication_date 2020/11/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let \Σ be a closed surface of genus least two and \ρ colon\n\π₁(\Σ) \→ G a Hitchin representation into\nG=\PSL(n,\ℝ), \PSp(2n,\ℝ), \PSO(n,n+1)\nor \G₂. We consider the energy functional E on the Teichm "uller\nspace of \Σ which assigns to each point in \T(\Σ) the\nenergy of the associated \ρ-equivariant harmonic map. The main result of\nthis paper is that E is strictly plurisubharmonic. As a corollary we obtain\nan upper bound of 3 \⋅ \genus(\Σ) -3 on the index of any\ncritical point of the energy functional.\n

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