Handbook of Geometric Analysis

Numerical Approximations to Extremal Metrics on Toric Surfaces R. S. Bunch, Simon K. Donaldson I 1 Introduction 2 The set-up 2.1 Algebraic metrics 2.2 Decomposition of the curvature tensor 2.3 Integration 3 Numerical algorithms: balanced metrics and refinedapproximations. 4 Numerical results 4.1 The hexagon 4.2 The pentagon 4.3 The octagon 4.4 The heptagon 5 Conclusions ReferencesKiihler Geometry on Toric Manifolds, and some other Manifolds withLarge SymmetryGlning Constructions of Special Lagrangian ConesHarmonic MappingsHarmonic Functions on Complete Riemannian ManifoldsComplexity of Solutions of Partial Differential EquationsVariational Principles on Triangulated SurfacesAsymptotic Structures in the Geometry of Stability and ExtremalMetricsStable Constant Mean Curvature SurfacesA General Asymptotic Decay Lemma for Elliptic ProblemsUniformization of Open Nonnegatively Curved K／ihler Manifolds inHigher DimensionsGeometry of Measures：Harmonic Analysis Meets Geometric MeasureTheoryThe Monge Ampere Eequation and its Geometric AapplicationsLectures on Mean Curvature Flows in Higher CodimensionsLocal and Global Analysis of Eigenfunctions on Riemannian ManifoldsYau’S Form of Schwarz Lemma and Arakelov Inequality On