Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class. Issue 4 (10th January 2017)

• Record Type: Journal Article
• Authors: Hall, Stuart James; Murphy, Thomas
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 60:Issue 4(2017)
• Page Start: 893
• Page End: 910
• Publication Date: 2017-01-10
• Subjects: extremal Kähler metric, -- Einstein metric, -- Ricci flow, -- linear stability; Primary 53C25, -- 53C55, -- Secondary 65N35; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091516000444
• Languages: English
• ISSNs: 0013-0915

Abstract

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.