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- W2566451135 abstract "The notion of finite type was developed by Kohn in the 1960's as a way of studying the 6d -Neumann problem on domains in Cn . Finite type is a biholomorphic invariant. This dissertation focuses on commutator type, developed J. Kohn, T. Bloom, and I. Graham, and variety type, developed by J. D'Angelo. Commutator type measures the differences between the real and complex tangent spaces at a given boundary point of a domain in Cn . Variety type measures the order of contact between holomorphic curves and the boundary of a domain in Cn . These two notions are equivalent in C2 , but not in Cn . In Cn , commutator type is upper-semicontinuous, while variety type does not have this property. However, variety type is locally finite. The proof of local finiteness given by D'Angelo is based on the development of another notion of type, ideal type. Although ideal type is comparable to variety type, it does not measure the same geometric property. This dissertation develops a new notion of finite type, curve type, which measures the same geometric property measured by variety type. Curve type is developed to better understand the local finiteness of variety type. Curve type uses smooth curves within the boundary of the domain to measure the order of contact between holomorphic curves and the boundary of the domain. Curve type, like variety type, is defined for hypersurfaces. Curve type can also be defined for general varieties. This dissertation defines curve type and compares curve type to variety type and commutator type. Equivalence between the three notions of type on hypersurfaces will be proven in C2 . The difference between curve type and variety type for varieties will be discussed in several examples. The equivalence between curve type and variety type in Cn will be proven. Finally, local finiteness of curve type and variety type will be discussed." @default.
- W2566451135 created "2017-01-06" @default.
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- W2566451135 date "2004-01-01" @default.
- W2566451135 modified "2023-09-27" @default.
- W2566451135 title "Commutator, curve, and variety type: an investigation of finite type in several complex variables" @default.
- W2566451135 hasPublicationYear "2004" @default.
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