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 Advanced Studies in Pure Mathematics 2002; 259 pp; hardcover Volume: 34 ISBN-10: 4-931469-18-3 ISBN-13: 978-4-931469-18-1 List Price: US$79 Member Price: US$63.20 Order Code: ASPM/34 The 1998-1999 program year of the Japan-U.S. Mathematics Institute at the Johns Hopkins University (Baltimore, MD) was devoted to minimal surfaces, geometric analysis, and symplectic geometry. The program culminated in a week-long workshop and conference to discuss recent developments. This volume is a collection of articles written by the speakers. It presents extended or modified versions of the lectures delivered at the meeting. Each article provides a vivid account of current research. The information given ranges from introductory-level to the most recent results. Of special interest is a long survey article by K. Fukaya on applications of Floer homology to mirror symmetry. Also discussed are new developments on the geometry of constant mean curvature one surfaces in hyperbolic 3-spaces of finite total curvature. The range of topics covered in the volume provides direction for further research in these rapidly developing areas. The book is suitable for graduate students and researchers interested in differential and symplectic geometry. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and researchers interested in differential and symplectic geometry. Table of Contents M. Cai -- Volume minimizing hypersurfaces in manifolds of nonnegative scalar curvature P. Collin, L. Hauswirth, and H. Rosenberg -- The Gaussian image of mean curvature one surfaces in $$\mathbb{H}^3$$ of finite total curvature H. Donnelly -- Behavior of eigenfunctions near the ideal boundary of hyperbolic space K. Fukaya -- Floer homology and mirror symmetry II M. Ghomi -- Solution to the shadow problem in 3-space H. Hashimoto, K. Mashimo, and K. Sekigawa -- On 4-dimensional CR-submanifolds of a 6-dimensional sphere M. Kokubu -- On isotropic minimal surfaces in Euclidean space H. Konno -- The topology of toric hyper-Kähler manifolds R. López -- Cyclic hypersurfaces of constant curvature J. McCuan -- A generalized height estimate for H-graphs, Serrin's corner lemma, and applications to a conjecture of Rosenberg J. Masamune and W. Rossman -- Discrete spectrum and Weyl's asymptotic formula for incomplete manifolds H. Ohta -- Brieskorn manifolds and metrics of positive scalar curvature K. Ono -- Space of geodesics on Zoll three-spheres W. Rossman, M. Umehara, and K. Yamada -- Constant mean curvature 1 surfaces with low total curvature in hyperbolic 3-space T. Takakura -- A note on the symplectic volume of the moduli space of spatial polygons