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Session 5. Complex Analysis
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The core of a complex manifold |
Tobias Harz, University of Wuppertal, Germany
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This talk is based on joint work with N. Shcherbina and G. Tomassini
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The core \(\mathfrak{c}(\mathcal{M})\) of a complex manifold
\(\mathcal{M}\) is introduced as the set of all points where every
smooth and bounded from above plurisubharmonic function on
\(\mathcal{M}\) fails to be strictly plurisubharmonic.
I will explain that every strictly pseudoconvex domain \(\Omega
\subset \mathcal{M}\) with smooth boundary admits a global defining
function that is strictly plurisubharmonic precisely in the
complement of \(\mathfrak{c}(\Omega)\). Moreover, I will discuss
properties of the core, in particular
- 1-pseudoconcavity of the core, and
- Liouville type properties of the core.
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