Geometric Properties of a General Kohn–Nirenberg Domain in ℂn - Kejia Hu; Hongyi Li; Di Zhao; Yuan Jiang; Baozhu Li (Mathematics)
The Kohn–Nirenberg domains are unbounded domains in <semantics>Cn</semantics>. In this article, we modify the Kohn–Nirenberg domain <semantics>ΩK,L=<mfenced separators="" open="{" close="">(z1,…,zn)</mfenced>∈Cn:Rezn+g∣zn∣2+<msubsup>∑j=1n−1</msubsup>(∣zj∣p+Kj∣zj∣p−qRe<msubsup>zjq</msubsup>+Lj∣zj∣p−2qIm<msubsup>zj2q</msubsup>)<0}</semantics> and discuss the existence of supporting surface and peak functions at the origin.