ScalingStacks

Theorem 1.1 . [020D]

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Theorem 1.1.

If (M,ωφ)(M,\omega_{\varphi}) is a cscK metric, where ωφ=ω0+−1​∂∂¯​φ\omega_{\varphi}=\omega_{0}+\sqrt{-1}\partial\bar{\partial}\varphi, then all higher derivatives of the Kähler potential φ\varphi can be estimated in terms of an upper bound of ∫Mlog⁡(ωφnω0n)​ωφn\int_{M}\log\big(\frac{\omega_{\varphi}^{n}}{\omega_{0}^{n}}\big)\omega_{\varphi}^{n}.

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