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Спутники
РН
SpaceX
Роскосмос
NASA
СпутникиРНSpaceXРоскосмосNASAThis dissertation investigates rigidity in several complex variables through the study of intrinsic metrics on bounded domains in Cn. In particular, it focuses on geometric and analytic characterizations of the unit ball using the Carathéodory, Kobayashi, and Bergman metrics. These metrics are biholomorphically invariant and play a central role in understanding the complex geometry of domains independently of coordinate representations. The work is motivated by classical results of Lempert and Lu, as well as more recent developments concerning strongly pseudoconvex domains and curvature rigidity. The first main contribution concerns the Kähler structure of the Carathéodory metric on bounded strongly pseudoconvex domains. Lempert proved that on bounded convex domains the Carathéodory and Kobayashi metrics coincide, and an important consequence is that the Kobayashi metric is Kähler if and only if the domain is biholomorphic to the unit ball. More recently, Zimmer extended this...