Minimizing weak solutions for Calabi’s extremal metrics on toric manifolds. (English) Zbl 1141.53061
Summary: In this paper, we discuss Donaldson’s version of the modified \(K\)-energy associated to Calabi’s extremal metrics on toric manifolds and prove the existence of the weak solution for extremal metrics in the sense of convex functions which minimizes the modified \(K\)-energy.
MSC:
| 53C43 | Differential geometric aspects of harmonic maps |
| 32J15 | Compact complex surfaces |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 58E11 | Critical metrics |
References:
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