Thomas Pawlaschyk

collaborators

5 papers

math.CV2026

The Perron-Bremermann envelope for $q$ -plurisubharmonic functions on unbounded domains in $C^{n}$

Thomas Pawlaschyk

Let $D$ be an unbounded domain in $C^{n}$ , and let $f$ be a bounded continuous function prescribed on the boundary of $D$ . We show that, if $D$ has $r$ -peak points on its bo…

math.CV2025

On rigid $q$ -plurisubharmonic functions and $q$ -pseudoconvex tube domains in $C^{n}$

Thomas Pawlaschyk

In the spirit of Lelong and Bochner, we show that an upper semi-continuous function defined on a open tube set $I^c ◯ = I ¨ + i R^{n}$ in $C^{n}$ , where $I ¨ $ is an open set i…

math.CV2025

A Selection Theorem for the CarathÃ©odory Kernel Convergence of Pointed Domains

Kang-Tae Kim, Thomas Pawlaschyk

We present a selection theorem for domains in $C^{n}$ , $n \geq 1$ , which states that any tamed sequence of pointed connected open subsets admits a subsequence convergent to it…

math.CV2025

Foliations of continuous q-pseudoconcave graphs

Thomas Pawlaschyk, Nikolay Shcherbina

We show that for $k = 0, 1$ the graph of a continuous mapping $f : D \to R^{k} \times C^{p}$ , defined on a domain $D$ in $C^{n} \times R^{k}$ , is locally foli…

math.CV2025

On compact sets possessing $q$ -convex functions

Thomas Pawlaschyk, Nikolay Shcherbina

We show that there exists a $q$ -convex function in a neighborhood of a compact set $K$ in a complex manifold $M$ if and only if the $q$ -nucleus of this compact set is emp…

The Perron-Bremermann envelope for q-plurisubharmonic functions on unbounded domains in Cn

On rigid q-plurisubharmonic functions and q-pseudoconvex tube domains in Cn

A Selection Theorem for the CarathÃ©odory Kernel Convergence of Pointed Domains

Foliations of continuous q-pseudoconcave graphs

On compact sets possessing q-convex functions

The Perron-Bremermann envelope for $q$ -plurisubharmonic functions on unbounded domains in $C^{n}$

On rigid $q$ -plurisubharmonic functions and $q$ -pseudoconvex tube domains in $C^{n}$

On compact sets possessing $q$ -convex functions