Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On smoothing of plurisubharmonic functions on unbounded domains (2104.14448v1)

Published 29 Apr 2021 in math.CV

Abstract: We prove that for every $n \ge 2$, there exists a pseudoconvex domain $\Omega \subset \mathbb{C}n$ such that $\mathfrak{c}0(\Omega) \subsetneq \mathfrak{c}1(\Omega)$, where $\mathfrak{c}k(\Omega)$ denotes the core of $\Omega$ with respect to $\mathcal{C}k$-smooth plurisubharmonic functions on $\Omega$. Moreover, we show that there exists a bounded continuous plurisubharmonic function on $\Omega$ that is not the pointwise limit of a sequence of $\mathcal{C}1$-smooth bounded plurisubharmonic functions on $\Omega$.

Summary

We haven't generated a summary for this paper yet.