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Hölder continuity of solutions to the complex Monge-Ampère equation with the right-hand side in \(L^{p}\): the case of compact Kähler manifolds. (English) Zbl 1149.32018

Let \(M\) be a compact \(n\)-dimensional Kähler manifold with the fundamental form \(\omega\). On this manifold the author considers a solution of the Monge-Ampère equation
\[ (\omega + d d^c u)^n = f \omega^n, \]
where \(f \in L^p (M), p > 1; f \geq 0;\)
\[ \int_M f \omega^n = \int_M \omega^n \]
is a given function. He proves that the solution \(u\) of this equation is Hölder continuous (Theorem 2.1).

MSC:

32U05 Plurisubharmonic functions and generalizations
32U40 Currents
32W20 Complex Monge-Ampère operators
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References:

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