We exhibit two applications of Schwarz lemmas in several complex variables. The
first application extends Fornæss and Stout’s theorem on monotone unions
of balls to monotone unions of ellipsoids. The second application extends
Yang’s theorem on bidiscs to the generalized bidisc defined by the author
in his previous work. These applications reveal a connection between the
geometry of domains and their curvatures. The proof contains a careful study of
biholomorphisms, a detailed analysis on convergences, and a modified argument of
Yang.
Keywords
the Schwarz lemma, applications, the generalized bidisc,
ellipsoids
