Weil-Petersson geometry for families of hyperbolic conical Riemann surfaces

DOI10.1307/mmj/1301586301zbMath1223.30014arXiv0809.0058OpenAlexW2963217996MaRDI QIDQ538005

Stefano Trapani, Georg Schumacher

Publication date: 23 May 2011

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.0058

zbMATH Keywords

Weil-Petersson geometryconical Riemann surfaces

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Fine and coarse moduli spaces (14D22)

Related Items (3)

Constant Gauss curvature foliations of AdS spacetimes with particles ⋮ Riemann-Roch isometries in the non-compact orbifold setting ⋮ The convex core of quasifuchsian manifolds with particles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The moduli space of extremal compact Kähler manifolds and generalized Weil-Petersson metrics
• Weil-Petersson volumes and cone surfaces
• Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces
• Chern forms and the Riemann tensor for the moduli space of curves
• Determinants of Cauchy-Riemann operators on a Riemann surface
• On a natural algebraic affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil-Petersson metric
• Les surfaces euclidiennes à singularités coniques. (Euclidean surfaces with cone singularities)
• Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
• Prescribing curvature on open surfaces
• A direct approach to the determination of Gaussian and scalar curvature functions
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Prescribed curvature and singularities of conformal metrics on Riemann surfaces
• Moduli spaces of weighted pointed stable curves.
• Curvature functions for compact 2-manifolds
• Geometric approach to the Weil-Petersson symplectic form
• Generalizations of McShane's identity to hyperbolic cone-surfaces
• Curvature properties of Teichmüller's space
• Variation of cone metrics on Riemann surfaces
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Weil-Petersson volumes and intersection theory on the moduli space of curves
• On the Weil-Petersson Metric on Teichmuller Space
• Point Singularities and Conformal Metrics on Riemann Surfaces
• On a Class of Conformal Metrics
• Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on ℳ_{0,𝓃}
• Curvature functions for 2-manifolds with negative Euler characteristic

This page was built for publication: Weil-Petersson geometry for families of hyperbolic conical Riemann surfaces