Prospects in Complex Geometry Proceedings of the 25th Taniguchi International Symposium held in Katata, and the Conference held in Kyoto, July 31 - August 9, 1989

In the Teichmüller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years. Thus the central subject of "Complex Structure" was a timely choice for the joint meetings in Katata and Kyoto in 1989. The invited participants exchanged ideas on different approaches to related topics in complex geometry and mapped out the prospects for the next few years of research.

Hyperkähler structure on the moduli space of flat bundles.- Hardy spaces and BMO on Riemann surfaces.- Application of a certain integral formula to complex analysis.- On inner radii of Teichmüller spaces.- On the causal structures of the silov boundaries of symmetric bounded domains.- The behavior of the extremal length function on arbitrary Riemann surface.- A strong harmonic representation theorem on complex spaces with isolated singularities.- Mordell-Weil lattices of type E8 and deformation of singularities.- The spectrum of a Riemann surface with a cusp.- Moduli spaces of harmonic and holomorphic mappings and diophantine geometry.- Global nondeformability of the complex projective space.- Some aspects of hodge theory on non-complete algebraic manifolds.- Lp-Cohomology and satake compactifications.- Harmonic maps and Kähler geometry.- Complex-analyticity of pluriharmonic maps and their constructions.- Higher eichler integrals and vector bundles over the moduli of spinned Riemann surfaces.