Contents (* denotes one-hour survey lectures) Preface xix PART 1 Open Problems in Geometry* SHING TUNG YAU 1 Questions and Answers about Area-Minimizing Surfaces and Geometric Measure Theory* FRED 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 K-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 DETURCK 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 HARDT 141
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