Numerical approximations to extremal toric K "ahler metrics with\n arbitrary K "ahler class

2014/07/04 by Stuart James Hall, Hall, Stuart James, Thomas E. Murphy +1
Mathematics · #Geometry and complex manifolds #Meromorphic and Entire Functions #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1407.1272

Abstract

We develop new algorithms for approximating extremal toric K "ahler metrics.\nWe focus on an extremal metric on\n mathbbCP² sharp2\ mathbbCP², which is conformal to an\nEinstein metric (the Chen-LeBrun-Weber metric). We compare our approximation to\none given by Bunch and Donaldson and compute various geometric quantities. In\nparticular, we demonstrate a small eigenvalue of the scalar Laplacian of the\nEinstein metric which gives a numerical evidence that the Einstein metric is\nconformally unstable under the Ricci flow.\n

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