Geometry From the Pacific Rim : Proceedings of the Pacific Rim Geometry Conference Held at National University of Singapore, Republic of Singapore, December 12-17, 1994

played host to the Pacific Rim Geometry Conference-Singapore, 1994. This event was prompted by the success of a similar meeting in Hong Kong just two years earlier; many of its participants had urged the setting up of an arithmetic progression of such gatherings. Some 122 researchers from 15 different countries (including several remote from the shores of the Pacific) attended the conference. As indicated in the following pages, there were 11 invited, and a further 38 contributed, lectures on topics ranging from geometric analysis and differential geometry to algebraic geometry and topology. We are pleased to present herein research and expository articles contributed by a significant proportion of the participants, including almost all of the invited speakers. All contributions have been refereed: referees' very high praise for a number of the papers is most gratifying. As well as thanking the referees for their valuable efforts, we would also like to record our gratitude to those who were responsible for such a successful conference. Gauss-Manin connexions, logarithmic forms and hypergeometric functions Laws of trigonometry in symmetric spaces Determinants and extremal metrics in conformal geometry The infinity behavior of the solutions to the harmonic map heat equation On the absence of critical dimensions for the subelliptic Laplacian on the Heisenberg Group Minimal triangulation, complementarity and projective planes Compact infrasolvmanifolds are smoothly rigid Informal note on topology, geometry and topological field theory Singularity theory for Riemannian distance functions on non-positively curved surfaces The Gromov-Lawson-Rosenberg conjecture: when do manifolds admit metrics of positive scalar curvature Geometry of the Radon-Penrose transform and interpretation of singularities Realization in the large in R3 of surfaces Borsuk-Ulam type theorems and systems of bilinear equations Generalized affine rotation surfaces with geodesic orbits Lower bounds on some geometric quantities and applications Wavelet geometric analysis of the Dirichlet problem Moser’s inequality and n-Laplacian Submanifolds of a Riemannian manifold with semisymmetric recurrent connections Frénet theorem for spaces of constant curvature The generalized theorem of Castelnuovo-de Franchis for unitary representations Poisson and symplectic geometry on loop spaces of smooth manifolds An algebraic geometry view of a model quantum field theory on a curve Deforming convex hypersurfaces by the linear combination of the mean curvature and the square root of the scalar curvature Asymptotics for exterior solutions of quasilinear elliptic equations External geometry of p-minimal surfaces Geometry of torus quasi bundles over curves Stability of minimal graphs in products of surfaces Log Fano threefolds and quotients of Κ3 surfaces On certain Laplace inequalities on manifolds List of Participants List of Contributors

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.