Workshop on Theoretical and Numerical Aspects of Geometric Variational Problems

Canberra, September 24-28, 1990

Volume 26 in the Proceedings of the Centre for Mathematics and its Applications

Preface

This volume contains the proceedings of a seminar week of invited talks associated with the Workshop "Theoretical and Numerical Aspects of Geometric Variational Problems". The Workshop was conducted between August and Ocotber 1990; the seminar week was held from September 24 to 28.

The workshop brought together researchers primarily from Australia and Germany working in theoretical and applied mathematcs, numerical analysis and computer simulation. Particular emphasis was put on the graphical visualisation of geometric data. Many of the participants expressed their pleasure at the extent of the interaction between researchers in different but related fields.

The workshop was supported by the Department of Industry, Technology and Commerce (DITAC), through the Bilateral Science and Technology Program; by the German Research Foundation (DFG), Bonn; and by the Sonderforschungbereich SFB 256, Bonn University. The workshop was held at the Centre for Mathematical Analysis at the Australian National University with the assistance of the Centre and the Department of Mathematics.

The organisers would like to thank all participants for their role in the success of the meeting. Particular thanks are due to Marilyn Gray and Jill Smith for their extensive help towards the smooth running and friendly atmosphere of the workshop.

Gerd Dziuk (University of Freiburg), Gerhard Huisken (ANU) and John Hutchinson (ANU)
(Editors)

Contents

Preface
Flow of hypersurfaces by curvature functions Ben Andrews	1
Variational techniques and open problems in the recovery of surface shape from image shading M.J. Brooks	11
On entire solutions of the p-Laplacian J. Chabrowski	27
Discrete norms for the convergence of boundary integral methods G.A. Chandler	62
Recent existence and uniqueness results in shading analysis W. Chojnacki	79
On singular variational problems Ulrich Dierkes	89
Local techniques for mean curvature flow Klaus Ecker	107
A geometric measure theory approach to exterior problems for minimal surfaces Michael Grüter	120
Singularity formation in geometric evolution equations Gerhard Huisken	128
Computing conformal maps and minimal surfaces John Hutchinson	140
Second order elliptic equations with Venttsel boundary conditions Yousong Luo	162
Variational properties of some simple boundary integral equations W. McLean	168
Some topical variational geometry problems in computer graphics G.N. Newsam	179
Local spline approximants Andrew H. Norton	195
New periodic minimal surfaces in H3 Konrad Polthier	201
Hierarchical N-body calculations Stephen Roberts	211
Soliton geometry, Kac-Moody algebras and the Yang-Baxter equations Ivan Sterling	225
Crystalline geometric crystal growth Jean E. Taylor	231
Further existence results for two point boundary value problems arising in electro-diffusion H.B. Thompson	235
Plateau's problem for minimal surfaces with a catenoidal end Friedrich Tomi	240
Boundary regularity for the solution of the equation of prescribed mean curvature John I.E. Urbas	248
Least gradient problems Graham Williams	255
Compensated compactness and the biting lemma Kewei Zhang	265