## 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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