Extremal Hermitian metrics on Riemann surfaces with singularities

DOI10.1215/S0012-7094-00-10421-8zbMath0980.58009MaRDI QIDQ1580256

Xiaohua Zhu, Guofang Wang

Publication date: 27 February 2002

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

zbMATH Keywords

cuspenergy functionalconical singularityextremal Hermitian metric

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Critical metrics (58E11)

Related Items (16)

A complete conformal metric of preassigned negative Gaussian curvature for a punctured hyperbolic Riemann surface ⋮ HCMU surfaces and Weingarten surfaces ⋮ Multi-valued holomorphic functions and non-CSC extremal Kähler metrics with singularities on compact Riemann surfaces ⋮ On the existence of non-CSC extremal Kähler metrics with finite singularities on \(S^2\) ⋮ On one-dimensional and singular Calabi's extremal metrics whose Gauss curvatures have nonzero umbilical Hessians ⋮ A one-dimensional singular non-CSC extremal Kähler metric can be isometrically imbedded into \(\mathbb{R}^3\) as a Weingarten surface ⋮ Non-CSC extremal Kähler metrics on \(S^2_{\{2,2,2\}}\) ⋮ Super-Liouville Equations on Closed Riemann Surfaces ⋮ The affine Cauchy problem ⋮ Metrics of constant curvature on a Riemann surface with two corners on the boundary ⋮ Local isometric imbedding of a compact Riemann surface with a singular non-CSC extremal Kähler metric into 3-dimension space forms ⋮ Non-removable singularities of a fourth-order nonlinear partial differential equation ⋮ Extremal Kähler metrics and energy functionals on projective bundles ⋮ Variation of cone metrics on Riemann surfaces ⋮ Explicit isometric immersions from footballs to \(\mathbb{R}^3\) ⋮ On minimal immersions of a singular non-CSC extremal Kähler metric into 3-dimensional space forms

Cites Work

• Conformal deformations of metric on \({\mathcal S}\) 2
• The existence of minimal immersions of 2-spheres
• Prescribing Gaussian curvatures on surfaces with conical singularities
• Classification of solutions of some nonlinear elliptic equations
• Extremal Hermitian metrics on Riemann surfaces
• Qualitative properties of solutions to some nonlinear elliptic equations in \(\mathbb{R}^2\)
• Weak limits of Riemannian metrics in surfaces with integral curvature bound
• Metrics of constant curvature 1 with three conical singularities on the 2-sphere
• Extremal metrics of zeta function determinants on 4-manifolds
• What kinds of singular surfaces can admit constant curvature?
• Energy identity for a class of approximate harmonic maps from surfaces
• Curvature functions for compact 2-manifolds
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Point Singularities and Conformal Metrics on Riemann Surfaces
• Liouville Equation and Spherical Convex Polytopes
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