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Calabi $C^3$ estimate
I have a question regarding a computation analogous to the Calabi $C^3$ estimate which is used in the proof of the Calabi--Yau theorem.
Motivation: Establishing Liouville type theorems for complex ...
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4
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Unique Kahler-Einstein metric $g$ with $\mathrm{Ricc}(g)=-g$ when first Chern class $C_1(M)<0$: $\mathrm{Ricc}(h)=-g\,\Rightarrow\,h=cg$ for $c>0$?
On a compact Kahler manifold, let $g$ be the unique Kahler-Einstein metric with $\mathrm{Ricc}(g)=-g$, proved to exist by Yau and Aubin when the first Chern class $C_1(M)<0$.
Question: Does $g$ ...
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