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On the lower bounds of the $L^2$-norm of the Hermitian scalar curvature
Journal of Symplectic Geometry  (IF0.707),  Pub Date : 2020-01-01, DOI: 10.4310/jsg.2020.v18.n2.a5
Julien Keller, Mehdi Lejmi

On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-K\"ahler metrics, is actually an asymptotic invariant. This allows us to deduce a lower bound for the L^2-norm of the Hermitian scalar curvature as obtained by S. Donaldson \cite{Don} in the K\"ahler case.