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Lower bounds on the Calabi functional

S. K. Donaldson
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Abstract

The main result of this paper shows that "test configurations" give new lower bounds on the $L^{2}$ norm of the scalar curvature on a Kahler manifold. This is closely analogous to the analysis of the Yang-Mills functional over Riemann surfaces by Atiyah and Bott. The proof uses asymptotic approximation by finite-dimensional problems: the essential ingredient being the Tian-Zelditch-Lu expansion of the "density of states" function.

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S. K. Donaldson. 2005-06-24. Lower bounds on the Calabi functional. https://arxiv.org/abs/math/0506501

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