@book {IOPORT.00053783,
    editor       = {Wu, Hung-Hsi},
    title        = {Contemporary geometry: J.-Q. Zhong memorial volume.},
    year         = {1991},
    isbn         = {0-306-43742-2},
    pages        = {xi, 483 p.},
    publisher    = {New York etc.: Plenum Press},
    abstract     = {The articles of this volume will not be reviewed individually. The volume is dedicated to the memory of the Chinese mathematician Jia- Qing Zhong (1937-1987). Its main part contains a selection of his papers (numbered [4]--[17]) most of which so far have been available only in Chinese. The work of J.-Q. Zhong covers three main topics: (1) Several complex variables and complex differential geometry, in particular Hermitian symmetric spaces and bounded homogeneous domains, (2) harmonic analysis and group representations, (3) eigenvalue estimates of the Laplacian, in particular lower bounds for $\lambda\sb 1$. The first part of the volume gives some mathematical background for Zhong's work. It contains three survey articles: [1] by {\it P. Li} and {\it A. Treibergs} on eigenvalues of the Laplacian, [2] by {\it Qi-Keng Lu} on the development of complex analysis and geometry in China since 1948, and [3] by {\it Y.-T. Siu} on uniformization theory in several complex variables. All three articles include extended bibliographies. Unfortunately, a survey article covering Zhong's work on Lie algebras, group representations and Schubert calculus [4,5,8,9,16,17] is missing. In [1], several methods of obtaining upper and lower estimates for the eigenvalues of $\Delta$ and the relations to geometric problems (Willmore problem, isoperimetric inequality, stability of minimal surfaces) are discussed. One of Zhofg's contribution to this field is the sharp estimate $\lambda\sb 1\ge\pi\sp 2/d\sp 2$ for a compact manifold of diameter $d$ with nonnegative Ricci curvature [14], improving a result of Li and Yau. The main topics of [2] are homogeneous bounded domains in $\bbfC\sp n$ and symmetric spaces. One of the merits of this article is giving explicit matrix representations for all classical (non-exceptional) symmetric spaces. In particular, noncompact Hermitian symmetric spaces are embedded as an ``absolute domain'' $D$ into their compact dual symmetric spaces $X$ (``extension space''); this means that the automorphism group of $D$ consists precisely of all biholomorphic automorphisms of $X$ which leave $D$ invariant. From these explicit representations, J.-Q. Zhong had derived geometric data such as Busemann functions or certain holomorphic vector fields which are used for computing the cohomology [12]. Siu's article [3] treats the problem under which assumptions a given complex manifold is biholomorphic to an Hermitian symmetric space. Topological and curvature conditions are discussed which characterize Hermitian symmetric spaces of compact and noncompact type and $\bbfC\sp n$. A central topic are the rigidity and superrigidity theorems for noncompact type which mainly apply harmonic maps and the Bochner-Kodaira technique in order to pass from ``harmonic'' to ``holomorphic''; see also [13]. On the other side there are curvature characterizations for compact type which generalize the Frankel conjecture (cf. also [15]). Further topics covered in [3] are deformations of Hermitian symmetric spaces, the nonexistence proofs for a complex structure on the six-sphere, higher rank rigidity and asymptotic flatness. The volume starts with a short biography of J.-Q. Zhong, written by H. H. Wu, which is very impressing. It gives some insight into the life of a scientist in the China of the 50's, 60's and 70's, in particular during the Cultural Revolution. Between 1965 and 1976, Zhong could keep up his research under very difficult physical conditions only by working in secrecy and isolation. The extremely unfavourable health conditions during that time eventually caused his untimely death in 1987.},
    reviewer     = {J.-H.Eschenburg (Augsburg)},
    identifier   = {00053783},
}