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Invariant theory in Cauchy-Riemann geometry and applications to the study of holomorphic mappings
Descriptive
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Text
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Title
Invariant theory in Cauchy-Riemann geometry and applications to the study of holomorphic mappings
SubTitle
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ETD_1903
Identifier
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051934
Language
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eng
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theses
Subject
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Topic
Mathematics
Subject
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(authority = ETD-LCSH)
Topic
Cauchy-Riemann equations
Subject
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(authority = ETD-LCSH)
Topic
Holomorphic mappings
Abstract
In 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.
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electronic resource
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v, 75 p.
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Note
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Ph.D.
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Includes bibliographical references (p. 72-74)
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by Yuan Zhang
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Zhang
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Yuan
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1980-
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author
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Yuan Zhang
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Huang
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Xiaojun
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Advisory Committee
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Xiaojun Huang
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Chanillo
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Sagun
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internal member
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Sagun Chanillo
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Song
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Jian
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internal member
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Jian Song
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Berhanu
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Shiferaw
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outside member
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Shiferaw Berhanu
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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school
OriginInfo
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2009
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2009-10
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xx
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Rutgers University Electronic Theses and Dissertations
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ETD
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
Identifier
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doi:10.7282/T36T0MTF
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work
Copyright
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Copyright protected
Notice
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Open
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Permission or license
Note
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Zhang
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Yuan
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Yuan Zhang
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Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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