Explicit description for the automorphism group of the Fornوss domain

Motivated by the Kohn–Nirenberg domain, J.E. Fornæss considered the germ of a domain near the origin in C 2 such that Ω t = { ( z , w ) ∈ C 2 : Re w + | z w | 2 + | z | 6 + t | z | 2 Re ( z 4 ) < 0 } to study the holomorphic peak function that is smooth up to the boundary (Fornæss, 1977 [6]). J.E. Fornæss proved that for 1 < t < 9 / 5 the domain Ω t does not admit a holomorphic function on Ω t that is C 1 up to the boundary and that peaks at the origin. We define Π ( z , w ) = ( e i π 2 z , w ) . In this paper, we prove that for 1 < t < 9 / 5 , the automorphism group of Ω t is equal to the set { Π k : k = 1 , 2 , 3 , 4 } .