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Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class

  • Stuart James Hall (a1) and Thomas Murphy (a2)

Abstract

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.

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