Minimal Surfaces, Geometric Analysis and Symplectic Geometry

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  • Format: Hardcover
  • Copyright: 2002-07-01
  • Publisher: Amer Mathematical Society

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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.

Table of Contents

Volume Minimizing Hypersurfaces in Manifolds of Nonnegative Scalar Curvaturep. 1
The Gaussian Image of Mean Curvature One Surface in H[superscript 3] of Finite Total Curvaturep. 9
Behavior of Eigenfunctions near the Ideal Boundary of Hyperbolic Spacep. 15
Floer Homology and Mirror Symmetry IIp. 31
Solution to the Shadow Problem in 3-Spacep. 129
On 4-dimensional CR-Submanifolds of a 6-dimensional Spherep. 143
On Isotropic Minimal Surfaces in Euclidean Spacep. 155
The Topology of Toric HyperKahler Manifoldsp. 173
Cyclic Hypersurfaces of Constant Curvaturep. 185
A Generalized Height Estimate for H-graphs, Serrin's Corner Lemma, and Applications to a Conjecture of Rosenbergp. 201
Discrete Spectrum and Weyl's Asymptotic Formula for Incomplete Manifoldsp. 219
Brieskorn Manifolds and Metrics of Positive Scalar Curvaturep. 231
Space of Geodesics on Zoll Three-Spheresp. 237
Constant Mean Curvature 1 Surfaces with Low Total Curvature in Hyperbolic 3-Spacep. 245
A Note on the Symplectic Volume of the Moduli Space of Spatial Polygonsp. 255
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