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The analysis improves Yau's C0 estimate for Kähler manifolds with zero Chern class, suggesting new bounds.
In this paper, a simplified exposition of the celebrated Aubin-Yau proof for the existence of Kähler-Einstein metrics is provided. For the case of a compact Kähler manifold with vanishing first Chern class, we improve Yau's celebrated C⁰ a priori estimate. Instead of relying on the L∞ norm of the Kähler potential F as in the original proof, we establish a new uniform bound for the solution to the Monge-Ampère equation that depends only on the Lᵖ norm of eF. This new approach to the C⁰ estimate offers an alternative method for establishing uniform bounds for solutions to complex Monge-Ampère equations.
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Jin Pan (2025) studied this question.
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