In the same year, his doctoral dissertation Die Charakterisierung von Regularitätsgebieten durch pseudokonvexe Funktionen was published, in which he solved a special case of the Levi problem.

[1] After returning to the United States, he was a mathematics researcher at the Institute for Advanced Study in Princeton (1955–57), and then appointed assistant professor at the University of Washington, Seattle (1957–58).

[1] On 16 May 1954, Bremermann married Maria Isabel Lopez Perez-Ojeda, a scholar of romance language and literature.

Anderson writes:[Bremermann] continued to develop mathematical modelling as a tool to understanding complex (especially biological) systems for the rest of his life.

[...] Hans Bremermann is not only remembered for his genius but also for his warmth, generosity, courage, integrity, humility, and love.