Plurisubharmonicity and geodesic convexity of energy function on Teichmueller space

DOI10.1512/iumj.2022.71.8818zbMath1502.30132arXiv1809.00255OpenAlexW4214829638MaRDI QIDQ5070108

Xueyuan Wan, Inkang Kim, Genkai Zhang

Publication date: 19 April 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.00255

zbMATH Keywords

Teichmüller spaceharmonic mapWeil-Petersson metric

Mathematics Subject Classification ID

Harmonic maps, etc. (58E20) Teichmüller theory for Riemann surfaces (30F60)

Cites Work

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• The Weil-Petersson Hessian of length on Teichmüller space
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• The Teichmüller theory of harmonic maps
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• Deformations of the scalar curvature
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• Geodesic length functions and the Nielsen problem
• Deformations of metrics and associated harmonic maps
• Dirichlet's energy on Teichmüller's moduli space and the Nielsen realization problem
• Plurisuperharmonicity of reciprocal energy function on Teichmüller space and Weil-Petersson metric
• Geometric approach to the Weil-Petersson symplectic form
• Some remarks on Teichmüller's space of Riemann surfaces
• Variation of geodesic length functions in families of Kähler-Einstein manifolds and applications to Teichmüller space
• Geodesic-Einstein metrics and nonlinear stabilities
• Holomorphic convexity of Teichmüller spaces
• On Homotopic Harmonic Maps
• Harmonic Mappings of Riemannian Manifolds
• The Nielsen realization problem

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