Miniconfrence on Geometry and Partial Differential Equations

Canberra, August 1-3, 1985

Volume 10 in the Proceedings of the Centre for Mathematical Analysis

Preface

This volume contains the proceedings of a miniconfrenece on geometry and partial differential equations held at the Australian National University in August, 1985.

We gratefully acknowledge the support of the contributors to this volume, as well as the superb organisational assistance of our secretary, Marilyn Gray, the excellent typing of Dorothy Nash, Norman Chin and Joyce Heinz and the editing assistance of David Cullen and Marty Ross.

Leon Simon, Neil S, Trudinger
(Editors)

Contents

Asymptotic behaviour near isolated singular points for geometric variational problems David Adams and Leon Simon	1
The gauss map of submersion Paul Baird	8
Remarks on multiple solutions of nonlinear equations E. N. Dancer	25
About some ill-posed problems E. Di Benedetto	32
Partial regularity for solutions of variational problems N. Fusco and J. E. Hutchinson	57
Degree theory and gaussian measure in infinite dimensions E. Getzler	68
Minimal surfaces with free boundaries S. Hildebrandt	78
Minimal surface description of crystal structures S. T. Hyde and Sten Andersson	89
A piecewise linear theory of minimal surfaces in 3-manifolds William Jaco and J. H. Rubinstein	99
Boundary regularity for solutions of quasi-linear elliptic equations Chi-ping Lau	111
Deforming riemannian metrics on the 2-sphere P. R. A. Leviton and J. H. Rubinstein	123
Boundary behaviour of solutions of elliptic equations in "bad" domains Gary M. Lieberman	128
The neumann problem for equations of monge-ampere type P. L. Lions, N. S. Trudinger and J. I. E. Urbas	135
When are singular integral operators bounded? Alan McIntosh	141
The topology of asymptotically euclidean static perfect fluid space time A. K. M. Masood-ul-Alam	150
A note on branched stable two-dimensional minimal surfaces Mario J. Micallef	157
Existence of minimal surfaces of bounded topological type in three-manifolds Jon T. Pitts and J. H. Rubinstein	163
Some fully non-linear parabolic partial differential equations S. J. Reye	177
Existence of willmore surfaces Leon Simon	187
Classification of minimizing hypersurfaces asymptotic to quadratic cones in R^(n+1) Leon Simon and Bruce Solomon	217
Overdetermined systems defined by complex vector fields Francois Treves	224
Regularity of the singular sets in immiscible fluid interfaces and solutions to other plateau-type problems Brian White	244
Best continuity at the boundary for solutions of the minimal surface equation Graham Williams	250
The regularity of weak solutions to parabolic systems Yan Ziqian	256