C o n t e n t s (* denotes one-hour survey lectures) Preface xxi PART 1 Open Problems in Geometry* SHING TUN G YAU 1 Questions and Answers about Area-Minimizing Surfaces and Geometric Measure Theory* FRE D ALMGREN 29 On the Geometrical Origin and the Solutions of a Degenerate Monge-Ampere Equation DAVID BAO AND TUDOR RATIU 55 Differential Geometry and the Design of Gradient Algorithms* ROGER W. BROCKETT 69 Spectral Geometry of F-Manifolds and its Application to Harmonic Maps YUAN-JEN CHIANG 93 Constructing Harmonic Maps into the Hyperbolic Space HYEONG IN CHOI AND ANDREJS TREIBERGS 101 Spherical Minimal Immersions of Spherical Space Forms DENNIS DETURC K AND WOLFGANG ZILLER 111 Banach Manifolds of Solutions to Nonlinear Partial Differential Equa- tions, and Relations with Finite-Dimensional Manifolds JOSEF DORFMEISTER 121 Some New Harmonic Maps ROBERT HARD T 141
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