【摘要】 本文主要涉及几类多复变Hartogs域上的度量与刚性.首先讨论有界对称域上的Hartogs域与其典则度量相关的加权Bergman核的展开式以及该典则度量为平衡度量的充要条件.其次给出几类多复变Hartogs域(如华罗庚域、Fock-Bargmann-Hartogs域和五面块(pentablock))上逆紧全纯映射的刚性结果.更多还原

【Abstract】 This paper mainly deals with the metrics and rigidity on some Hartogs-type domains in several complex variables. Firstly, we describe the Bergman kernel expansions of canonical metrics for the Hartogs domains over bounded symmetric domains, and we also obtain necessary and sufficient conditions for the canonical metrics to be balanced metrics. Secondly, we give the rigidity of proper holomorphic mappings on several Hartogs domains(i.e., Hua domains, Fock-Bargmann-Hartogs domains and pentablock).更多还原