Ebook: Contemporary Geometry: J.-Q. Zhong Memorial Volume

Early one morning in April of 1987, the Chinese mathematician J. -Q. Zhong died unexpectedly of a heart attack in New York. He was then near the end of a one-year visit in the United States. When news of his death reached his Chinese-American friends, it was immediately decided by one and all that something should be done to preserve his memory. The present volume is an outgrowth of this sentiment. His friends in China have also established a Zhong Jia-Qing Memorial Fund, which has since twice awarded the Zhong Jia-Qing prizes for Chinese mathematics graduate students. It is hoped that at least part of the reasons for the esteem and affection in which he was held by all who knew him would come through in the succeeding pages of this volume. The three survey chapters by Li and Treibergs, Lu, and Siu (Chapters 1-3) all center around the areas of mathematics in which Zhong made noteworthy contributions. In addition to putting Zhong's mathematical contributions in perspective, these articles should be useful also to a large segment of the mathematical community; together they give a coherent picture of a sizable portion of contemporary geometry. The survey of Lu differs from the other two in that it gives a firsthand account of the work done in the People's Republic of China in several complex variables in the last four decades.

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Content:
Front Matter....Pages i-xi
Zhong Jia-Qing (1937–1987)....Pages 1-13
Publications of Zhong Jia-Qing....Pages 15-17
Front Matter....Pages 19-19
Applications of Eigenvalue Techniques to Geometry....Pages 21-52
The Theory of Functions of Several Complex Variables in China from 1949 to 1989....Pages 53-93
Uniformization in Several Complex Variables....Pages 95-130
Front Matter....Pages 131-131
Harmonic Analysis on Rotation Groups: Abel Summability....Pages 133-152
Coxeter-Killing Transformations of Simple Lie Algebras....Pages 153-168
Dimensions of the Rings of Invariant Differential Operators on Bounded Homogeneous Domains....Pages 169-185
On Prime Ideals of the Ring of Differential Operators....Pages 187-212
On the Sum of Class Functions of Weyl Groups....Pages 213-238
The Trace Formula of the Weyl Group Representations of the Symmetric Group....Pages 239-261
Some Types of Nonsymmetric Homogeneous Domains....Pages 263-303
The Extension Spaces of Nonsymmetric Classical Domains....Pages 305-345
Cohomology of Extension Spaces for Classical Domains....Pages 347-366
The Degree of Strong Nondegeneracy of the Bisectional Curvature of Exceptional Bounded Symmetric Domains....Pages 367-375
The Estimate of the First Eigenvalue of a Compact Riemannian Manifold....Pages 377-388
Curvature Characterization of Compact Hermitian Symmetric Spaces....Pages 389-448
Schubert Calculus and Schur Functions....Pages 449-462
An Expansion in Schur Functions and Its Applications in Enumerative Geometry....Pages 463-479
Back Matter....Pages 481-483

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Content:
Front Matter....Pages i-xi
Zhong Jia-Qing (1937–1987)....Pages 1-13
Publications of Zhong Jia-Qing....Pages 15-17
Front Matter....Pages 19-19
Applications of Eigenvalue Techniques to Geometry....Pages 21-52
The Theory of Functions of Several Complex Variables in China from 1949 to 1989....Pages 53-93
Uniformization in Several Complex Variables....Pages 95-130
Front Matter....Pages 131-131
Harmonic Analysis on Rotation Groups: Abel Summability....Pages 133-152
Coxeter-Killing Transformations of Simple Lie Algebras....Pages 153-168
Dimensions of the Rings of Invariant Differential Operators on Bounded Homogeneous Domains....Pages 169-185
On Prime Ideals of the Ring of Differential Operators....Pages 187-212
On the Sum of Class Functions of Weyl Groups....Pages 213-238
The Trace Formula of the Weyl Group Representations of the Symmetric Group....Pages 239-261
Some Types of Nonsymmetric Homogeneous Domains....Pages 263-303
The Extension Spaces of Nonsymmetric Classical Domains....Pages 305-345
Cohomology of Extension Spaces for Classical Domains....Pages 347-366
The Degree of Strong Nondegeneracy of the Bisectional Curvature of Exceptional Bounded Symmetric Domains....Pages 367-375
The Estimate of the First Eigenvalue of a Compact Riemannian Manifold....Pages 377-388
Curvature Characterization of Compact Hermitian Symmetric Spaces....Pages 389-448
Schubert Calculus and Schur Functions....Pages 449-462
An Expansion in Schur Functions and Its Applications in Enumerative Geometry....Pages 463-479
Back Matter....Pages 481-483
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