Geometric Properties of a General Kohn–Nirenberg Domain in ℂ n

Kejia Hu, Hongyi Li (), Di Zhao, Yuan Jiang and Baozhu Li
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Kejia Hu: School of Electronics and Communication Engineering, Sun Yat-Sen University, Shenzhen 518107, China
Hongyi Li: School of Mathematical Science, Beihang University, Beijing 100191, China
Di Zhao: School of Mathematical Science, Beihang University, Beijing 100191, China
Yuan Jiang: School of Electronics and Communication Engineering, Sun Yat-Sen University, Shenzhen 518107, China
Baozhu Li: Hangzhou Institute of Technology, Xidian University, Hangzhou 311200, China

Mathematics, 2025, vol. 13, issue 7, 1-8

Abstract: The Kohn–Nirenberg domains are unbounded domains in C n . In this article, we modify the Kohn–Nirenberg domain Ω K , L = ( z 1 , … , z n ) ∈ C n : R e z n + g ∣ z n ∣ 2 + ∑ j = 1 n − 1 ( ∣ z j ∣ p + K j ∣ z j ∣ p − q R e z j q + L j ∣ z j ∣ p − 2 q I m z j 2 q ) < 0 } and discuss the existence of supporting surface and peak functions at the origin.

Keywords: Kohn–Nirenberg domain; peak function; supporting surface (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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