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Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 4 / November 2017
- Published online by Cambridge University Press:
- 10 January 2017, pp. 893-910
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- Article
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We develop new algorithms for approximating extremal toric Kähler metrics. We focus on an extremal metric on
, which is conformal to an Einstein metric (the Chen–LeBrun–Weber metric). We compare our approximation to one given by Bunch and Donaldson and compute various geometric quantities. In particular, we demonstrate a small eigenvalue of the scalar Laplacian of the Einstein metric that gives numerical evidence that the Einstein metric is conformally unstable under Ricci flow.
, which is conformal to an Einstein metric (the Chen–LeBrun–Weber metric). We compare our approximation to one given by Bunch and Donaldson and compute various geometric quantities. In particular, we demonstrate a small eigenvalue of the scalar Laplacian of the Einstein metric that gives numerical evidence that the Einstein metric is conformally unstable under Ricci flow.