Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 74-75).

Thesis (Ph.D.)--University of Wisconsin--Madison, 1964. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 75-76).

by Wong Sai Yiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 94-97). / Introduction --- p.iii / Chapter 1 --- Invariants on ideals of holomorphic function germs --- p.1 / Chapter 1.1 --- Preliminaries --- p.1 / Chapter 1.2 --- Ideals of holomorphic function germs --- p.3 / Chapter 1.3 --- The order of contact of an ideal --- p.7 / Chapter 1.4 --- Higher order invariants --- p.11 / Chapter 2 --- Geometry on real hypersurfaces of Cn --- p.14 / Chapter 2.1 --- CR geometry --- p.14 / Chapter 2.2 --- The associated family of holomorphic ideals on real subvaxiety of Cn --- p.18 / Chapter 2.3 --- Relationships between points of finite type and complex varieties --- p.25 / Chapter 2.4 --- The case of pseudoconvex real hypersurfaces --- p.33 / Chapter 2.5 --- Other finite type conditions --- p.35 / Chapter 3 --- Point of finite type and the d-Neumann problem --- p.44 / Chapter 3.1 --- Introduction --- p.44 / Chapter 3.2 --- Subellipticity and subelliptic multipliers --- p.47 / Chapter 3.3 --- Geometry on Kohn's ideals of subelliptic multipliers --- p.60 / Chapter 3.4 --- The Diederich - Fornaess theorem --- p.66 / Chapter 3.5 --- Catlin's necessary condition on subellipticity --- p.69 / Chapter 4 --- Analysis on finite type domains --- p.78 / Chapter 4.1 --- The Bergman projection --- p.78 / Chapter 4.2 --- Boundary regularity of proper holomorphic mappings --- p.83 / Chapter 4.3 --- Local regularity and extension of CR mappings --- p.88 / Bibliography --- p.94

Hui, Chun Yin. / On t.p. "n" is a superscript. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Basic properties of real hypersurfaces in CN --- p.9 / Chapter 2.1 --- Hypersurfaces in CN and some nondegeneracy conditions --- p.9 / Chapter 2.2 --- CR functions and their holomorphic extensions --- p.15 / Chapter 2.3 --- Normal coordinates for real analytic hypersurfaces --- p.18 / Chapter 3 --- The algebraic results for reflection principle --- p.22 / Chapter 4 --- Reflection principle for real analytic hypersurfaces in higher complex dimensions --- p.30 / Chapter 4.1 --- Reflection principle for Levi nondegenerate hypersurfaces --- p.31 / Chapter 4.2 --- Essentially finite real analytic hypersurfaces and not totally degenerate CR mappings --- p.38 / Chapter 4.3 --- Reflection principle for essentially finite hypersurfaces --- p.44 / Chapter 4.4 --- Reflection principle for CR mappings and bounded domains --- p.54 / Chapter 4.5 --- Futher results on the reflection principle --- p.64 / Chapter 5 --- An extension result of CR functions by a general Schwarz reflection principle --- p.66 / Chapter 5.1 --- A general Schwarz reflection principle --- p.66 / Chapter 5.2 --- "Holomorphic extension of CR functions on a real analytic, generic CR submanifold in CN" --- p.69 / Bibliography --- p.80

In this dissertation, we consider various aspects of the boundary behavior of holomorphic functions of several complex variables. In dimension one, a characterization of the radial limit zero sets of nonconstant holomorphic functions on the disc has been given by Lusin, Privalov, McMillan, and Berman. In higher dimensions, no such characterization is known for holomorphic functions on the unit ball B. Rudin posed the question as to the existence of nonconstant holomorphic functions on the ball with radial limit zero almost everywhere. Hakim, Sibony, and Dupain showed that such functions exist. Because the characterization in dimension one involves both Lebesgue measure and Baire category, it is natural to also ask whether there exist nonconstant holomorphic functions on the ball having residual radial limit zero sets. We show here that such functions exist. We also prove a higher dimensional version of the Lusin-Privalov Radial Uniqueness Theorem, but we show that, in contrast to what is the case in dimension one, the converse does not hold. We show that any characterization of radial limit zero sets on the ball must take into account the "complex structure" on the ball by giving an example that shows that the family of these sets is not closed under orthogonal transformations of the underlying real coordinates. In dimension one, using the theorem of McMillan and Berman, it is easy to see that radial limit zero sets are not closed under unions (even finite unions). Since there is no analogous result in higher dimensions of the McMillan and Berman result, it is not obvious whether the radial limit zero sets in higher dimensions are closed under finite unions. However, we show that, as is the case in dimension one, these sets are not closed under finite unions. Finally, we show that there are smooth curves of finite length in S that are non-tangential limit uniqueness sets for holomorphic functions on B. This strengthens a result of M. Tsuji.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 91-93).

Thesis Abstract In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical behavior of the composition of a pseudo-random sequence of H´enon mappings. In analogy with the dynamics of the iterates of a single H´enon map, it is possible to construct fibered Green functions that satisfy suitable invariance properties and the corresponding stable and unstable currents. Further, it is shown that the successive pullbacks of a suitable current by the skew H´enon maps converge to a multiple of the fibered stable current. Second part of the thesis generalizes most of the above-mentioned results for a com- pletely random sequence of H´enon maps. In addition, for this random system of H´enon maps, we introduce the notion of average Green functions and average Green currents which carry many typical features of the classical Green functions and Green currents. Third part consists of some results about the global dynamics of a special class of skew maps. To prove these results, we use the knowledge of dynamical behavior of pseudo- random sequence of H´enon maps widely. We show that the global skew map is strongly mixing for a class of invariant measures and also provide a lower bound on the topological entropy of the skew product. We conclude the thesis by studying another class of maps which are skew products of holomorphic endomorphisms of Pk fibered over a compact base. We define the fibered Fatou components and show that they are pseudoconvex and Kobayashi hyperbolic. 1

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

by Yeung Chung Kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 104-105). / Chapter 1 --- Infinitesimal Deformation of Compact Complex Manifolds --- p.3 / Chapter 1.1 --- Differentiable Family --- p.3 / Chapter 1.2 --- Infinitesimal Deformation in Differentiable Family --- p.6 / Chapter 1.3 --- Trivial Differentiable Family --- p.8 / Chapter 1.4 --- Complex Analytic Family --- p.13 / Chapter 1.5 --- Induced Family --- p.19 / Chapter 2 --- Theorem of Existence --- p.22 / Chapter 2.1 --- Introduction --- p.22 / Chapter 2.2 --- "Some Facts on the qth Cohomology Group Hq(M,´ة）" --- p.23 / Chapter 2.3 --- Obstructions to Deformation --- p.24 / Chapter 2.4 --- An Elementary Method for Theorem of Existence --- p.26 / Chapter 2.5 --- Proof of Theorem of Existence --- p.35 / Chapter 3 --- "Comparison between the Number of Moduli m(M) and dim H1 (M,´ة）" --- p.64 / Chapter 3.1 --- Number of Moduli of Compact Complex Manifold --- p.64 / Chapter 3.2 --- Examples --- p.68 / Chapter 4 --- Theorem of Completeness --- p.84 / Chapter 4.1 --- Theorem of Completeness --- p.84 / Chapter 4.2 --- Construction of Formal Power Series of h and g --- p.86 / Chapter 4.3 --- Proof of Convergence --- p.93