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### GAIA Seminar on Complex Analytic Geometry - Dr. Tobias Harz

posted Sep 24, 2015, 6:07 PM by Hyemin Shin   [ updated Sep 29, 2015, 9:16 PM ]

 - Title: Defining Functions and Cores of Unbounded Domains- Speaker: Dr. Tobias Harz (GAIA)- Abstract: I will explain that every unbounded strictly pseudoconvex domain $\Omega$ in a complex manifold admits a plurisubharmonic defining function, which is defined on a neighborhood of the closure $\bar{\Omega}$, and which is strictly plurisubharmonic near the boundary $b\Omega$. Investigation of the minimal subset of $\Omega$ where every such function fails to be strictly plurisubharmonic leads to the definition of the core $\mathfrak{c}(\Omega)$ of $\Omega$. I will prove that $\mathfrak{c}(\Omega)$ is always $1$-pseudoconcave in $\Omega$, and, if time permits, state some results on Liouville type properties of the core. This is joint work with N. Shcherbina and G. Tomassini.- Place: GAIA Seminar Room (#106, Math Science bldg.) - Date: 8 p.m. - 10 p.m on Monday, 5 October 2015Poster <----click