AG Komplexe Analysis: Thomas Pawlaschyk (D.13.15)
The $q$-pluriubharmonic functions form the upper semi-continuous analog of $(q+1)$-convex functions in the sense of Grauert. I will introduce $q$-plurisbuharmonic functions in $\mathbb{C}^n$ in the sense of Hunt-Murray and present the relation to $q$-pseudoconvex sets in the sense of Rothstein and Słodkowski. In my recent research, I investigated $q$-pseudoconvex tube domains in order to generalize the well-known results by Lelong, Bochner and Bremermann on the relation of rigid plurisubharmonic functions and pseudoconvex tube domains to convexity.
