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Recent Developments in Geometry
Edited by: S.-Y. Cheng, H. Choi, and Robert E. Greene
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Contemporary Mathematics
1990; 338 pp; softcover
Volume: 101
ISBN-10: 0-8218-5107-1
ISBN-13: 978-0-8218-5107-4
List Price: US$56
Member Price: US$44.80
Order Code: CONM/101
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This volume is the outgrowth of a Special Session on Geometry, held at the November 1987 meeting of the AMS at the University of California at Los Angeles. The unusually well-attended session attracted more than sixty participants and featured over forty addresses by some of the day's outstanding geometers. By common consent, it was decided that the papers to be collected in the present volume should be surveys of relatively broad areas of geometry, rather than detailed presentations of new research results. A comprehensive survey of the field is beyond the scope of a volume such as this. Nonetheless, the editors have sought to provide all geometers, whatever their specialties, with some insight into recent developments in a variety of topics in this active area of research.

Table of Contents

  • R. E. Greene -- Some recent developments in Riemannian geometry
  • R. Brooks -- Designer metrics on Riemannian manifolds
  • G. Walschap -- Open manifolds of nonnegative curvature
  • S. W. Wei -- An extrinsic average variational method
  • P. Aviles -- The Dirichlet problem and Fatou's theorem for harmonic mappings on regular domains
  • D. A. Hoffman -- New examples of singly-periodic minimal surfaces and their qualitative behavior
  • V. I. Oliker -- The Gauss curvature and Minkowski problems in space forms
  • Y. S. Poon -- Self-duality, twistor theory, its generalization and application
  • P. B. Gilkey -- Spectral geometry of Riemannian manifolds
  • M. A. Pinsky -- Eigenvalue asymptotics and their geometric applications
  • R. M. Tse -- A lower bound for the number of isospectral surfaces
  • S.-Y. A. Chang and P. C. Yang -- The conformal deformation equation and isospectral set of conformal metrics
  • J. Lott -- Analytic torsion for group actions
  • G. Knieper and H. Weiss -- Regularity of entropy for geodesic flows
  • G. R. Jensen and M. Rigoli -- Twistor and Gauss lifts of surfaces in four-manifolds
  • W. Gao -- Affine differential geometry of complex hypersurfaces
  • K.-T. Kim -- Domains with noncompact automorphism groups
  • S. Frankel -- Affine approach to complex geometry
  • N. Monk -- Compactification of complete Kähler-Einstein manifolds of finite volume
  • S. S.-T. Yau -- Topological types of isolated hypersurface singularities
  • T. Duchamp and M. Kalka -- Complex foliations
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