Harmonic maps of the moduli space of compact Riemann surfaces

DOI10.1007/BF01458616zbMath0601.32025MaRDI QIDQ1081002

Georg Schumacher

Publication date: 1986

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164161

zbMATH Keywords

harmonic mapWeil-Petersson metricstrong rigiditycompletion of moduli spaceRiemann surface with nodesSiu's curvature condition

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Real-valued functions on manifolds (58C05)

Related Items (16)

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures ⋮ On the rigidity of certain discrete groups and algebraic varieties ⋮ $C^1$ estimates for the Weil-Petersson metric ⋮ Growth of the Weil-Petersson inradius of moduli space ⋮ Curvature of the base manifold of a Monge-Ampère fibration and its existence ⋮ Curvature properties for moduli of canonically polarized manifolds -- an analogy to moduli of Calabi-Yau manifolds ⋮ Good geometry on the curve moduli ⋮ Spaces of Riemannian metrics ⋮ New results on the geometry of the moduli space of Riemann surfaces ⋮ The Weil-Petersson curvature operator on the universal Teichmüller space ⋮ Foliated Plateau problem. II: Harmonic maps of foliations ⋮ Positivity of relative canonical bundles and applications ⋮ Semigroup action on \(\mathbb T^n\) ⋮ Asymptotic flatness of the Weil-Petersson metric on Teichmüller space ⋮ The Weil–Petersson geometry of the moduli space of Riemann surfaces ⋮ On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces

Cites Work

• Unnamed Item
• The complex-analyticity of harmonic maps and the strong rigidity of compact Kaehler manifolds
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Theta functions on Riemann surfaces
• Curvature properties of Teichmüller's space

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