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Session 5. Complex Analysis
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The complex Hessian equations |
Sławomir Kołodziej, Jagiellonian University, Poland
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The talk is based on a joint work with S. Dinew
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I will present the existence and stability results for the complex
Hessian equations
\[
(dd^c u)^m \wedge \beta ^{n-m} =f \beta ^n,
\]
(\(\beta =dd^c |z|^2 \) and \(u\) is the unknown) in domains of
\(\mathbb C^n\) and
\[
(\omega + dd^c u)^m \wedge \omega ^{n-m} = f\omega ^n ,
\]
on a compact Kähler manifold \((X, \omega )\). I will focus on
the methods of pluripotential theory. They find also applications
in the study of other equations considered in complex geometry.
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