Minimizing weak solutions for calabi's extremal metrics on toric manifolds

Details Minimizing weak solutions for calabi's extremal metrics on toric manifolds Minimizing weak solutions for calabi's extremal metrics on toric manifolds

2006-11-04

arxiv.org/abs/math/0611099v1

Mathematics

Differential Geometry

28 pages, 3 figures

Scientific paper

In this paper, we discuss a Donaldson's version of the modified $K$-energy
associated to the 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.

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