University Mathematics

Zhong Jia-Qing (1937-1987).- Publications of Zhong Jia-Qing.- I: Surveys of Contemporary Geometry.- 1. Applications of Eigenvalue Techniques to Geometry.- 1.1. Eigenvalues of the Laplacian.- 1.2. Upper Bounds via Conformal Geometry.- 1.3. Upper Bounds Using Cheng's Comparison Theorem.- 1.4. Lower Bounds by Gradient Estimates.- 1.5. Isoperimetric Inequalities.- 1.6. A Lower Bound of Choi and Wang and Its Application to Minimal Surfaces.- 1.7. Nodal Domains and Multiplicity Bounds.- 1.8. Stability of Minimal Surfaces.- References.- 2. The Theory of Functions of Several Complex Variables in China from 1949 to 1989.- 2.1. The Classical Domains.- 2.2. The Classical Manifolds.- 2.3. Homogeneous Manifolds.- 2.4. Integral Representations and Their Boundary Values.- 2.5. The Schwarz Lemma.- 2.6. Harmonic Analysis in Classical Domains and on Their Characteristic Manifolds.- 2.7. Pseudoconvex Domains.- References.- 3. Uniformization in Several Complex Variables.- 3.1. Characterization of Compact Type by Topological Conditions.- 3.2. Characterization of Noncompact Type by Topological Conditions.- 3.3. Characterization of Compact Type by Curvature Conditions.- 3.4. Characterization of Noncompact Type by Curvature Conditions.- 3.5. Characterization of Euclidean Space by Curvature Conditions.- 3.6. Characterization of Noncompact Type by Compact Quotients.- 3.7. Metric Rigidity.- References.- II: Selected Papers of Zhong Jia-Qing.- 4. Harmonic Analysis on Rotation Groups: Abel Summability.- 5. Coxeter-Killing Transformations of Simple Lie Algebras.- 6. Dimensions of the Rings of Invariant Differential Operators on Bounded Homogeneous Domains.- 7. On Prime Ideals of the Ring of Differential Operators.- 8. On the Sum of Class Functions of Weyl Groups.- 9. The Trace Formula of the Weyl Group Representations of the Symmetric Group.- 10. Some Types of Nonsymmetric Homogeneous Domains.- 11. The Extension Spaces of Nonsymmetric Classical Domains.- 12. Cohomology of Extension Spaces for Classical Domains.- 13. The Degree of Strong Nondegeneracy of the Bisectional Curvature of Exceptional Bounded Symmetric Domains.- 14. On the Estimate of the First Eigenvalue of a Compact Riemannian Manifold.- 15. Curvature Characterization of Compact Hermitian Symmetric Spaces.- 16. Schubert Calculus and Schur Functions.- 17. An Expansion in Schur Functions and Its Applications in Enumerative Geometry.