Extremal metrics on toric surfaces

DOI10.1016/j.aim.2018.10.015zbMath1411.53054arXiv1008.2607OpenAlexW2963897646MaRDI QIDQ1621462

An-Min Li, Li Sheng, Bo Hui Chen

Publication date: 8 November 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.2607

zbMATH Keywords

extremal metricstoric surfacesAbreu equations

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15)

Related Items (22)

The HcscK equations in symplectic coordinates ⋮ Affine techniques on extremal metrics on toric surfaces ⋮ Extremal Kähler Poincaré type metrics on toric varieties ⋮ Differential inequalities on homogeneous toric bundles ⋮ Relative algebro-geometric stabilities of toric manifolds ⋮ Prescribed scalar curvatures for homogeneous toric bundles ⋮ Extremal metrics on toric manifolds and homogeneous toric bundles ⋮ Extremal Kähler metrics of toric manifolds ⋮ The global existence and convergence of the Calabi flow on \(\mathbb C^{n}/\mathbb Z^{n}+i \mathbb Z^{n}\) ⋮ Interior estimates for the \(n\)-dimensional Abreu's equation ⋮ Uniform K-stability for extremal metrics on toric varieties ⋮ Kähler–Einstein Metrics on Toric Manifolds and G-manifolds ⋮ The Monge-Ampère equation with Guillemin boundary conditions ⋮ On the constant scalar curvature Kähler metrics (II)—Existence results ⋮ The interior regularity of the Calabi flow on a toric surface ⋮ Note on scalar curvature of extremal Kähler metrics on \(\mathbb{C} P^2 \# 2 \overline{\mathbb{C} P^2}\) ⋮ A Bernstein property of a class of fourth order complex partial differential equations ⋮ Some estimates for the generalized Abreu equation ⋮ The stabilities of \(\mathbb{C} P^2 {\#} \overline{2 \mathbb{C} P^2} \) ⋮ Interior regularity for the generalized Abreu equation ⋮ Uniform K-stability and conformally Kähler, Einstein-Maxwell geometry on toric manifolds ⋮ A regularity theorem of the Abreu equation

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