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TitleInvariant theory in Cauchy-Riemann geometry and applications to the study of holomorphic mappings
NameZhang, Yuan (author), Huang, Xiaojun (internal member), Chanillo, Sagun (internal member), Song, Jian (internal member), Berhanu, Shiferaw (outside member), Rutgers University, Graduate School - New Brunswick,
Degree Date2009-10
Date Created2009
SubjectMathematics,
Cauchy-Riemann equations,
Holomorphic mappings
DescriptionIn this dissertation, proper holomorphic maps between some types of CR manifolds have been studied. For non-degenerate holomorphic Segre maps between Hn and HN , the complexifications of Heisenberg hypersurfaces, we show that they possess a partial
rigidity property when N ≤ 2n − 2. As an application under the same assumption, we prove that the holomorphic Segre non-transversality for these maps propagates along Segre varieties. this propagation property fails when N > 2n − 2. For any proper rational holomorphic map between complex balls, we derive a simple and explicit criterion when it is equivalent to a holomorphic polynomial map. This criterion is used to show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps. For general smooth CR embeddings from a Levi non-degenerate hypersurface into another one with the same signature, a monotonicity property of the
Chern-Moser-Weyl curvature along directions in the null space of the Levi-form has been obtained.
rigidity property when N ≤ 2n − 2. As an application under the same assumption, we prove that the holomorphic Segre non-transversality for these maps propagates along Segre varieties. this propagation property fails when N > 2n − 2. For any proper rational holomorphic map between complex balls, we derive a simple and explicit criterion when it is equivalent to a holomorphic polynomial map. This criterion is used to show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps. For general smooth CR embeddings from a Levi non-degenerate hypersurface into another one with the same signature, a monotonicity property of the
Chern-Moser-Weyl curvature along directions in the null space of the Levi-form has been obtained.
NotePh.D.
NoteIncludes bibliographical references (p. 72-74)
Noteby Yuan Zhang
Genretheses
Persistent URLhttp://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051934
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work