Theoretical and Numerical Aspects of Geometric Variational Problems


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 October 1990:  the seminar week was held from September 24 - 28.

The workshop brought together researchers primarily from Australia and Germany working in theoretical and applied mathematics, 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 extend 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; but the German Research Foundation (DFG), Bonn; and by the Sonderforchungbereich 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.


Chapter Page number
1 - Flow of Hypersurfaces by Curvature Functions (pdf 808.68 KB)
Ben Andrews
2 - Variational Techniques and Open Problems in the Recovery of Surface Shape from Image Shading (pdf 1.89 MB)
MJ Brooks
3 - On Entire solutions of the p-LAPLACIAN (pdf 2.12 MB)
J Chabrowski
4 - Discrete Norms for the Convergence of Boundary Intergral Methods (pdf 1.07 MB)
GA Chandler
5 - Recent Existence and Uniqueness Results in Shading Analysis (pdf 1.18 MB)
W Chojnacki
6 - On Singular Variational Problems (pdf 1.64 MB)
Ulrich Dierkes
7 - Local Techniques for Mean Curvature Flow (pdf 813 KB)
Klaus Ecker
8 - A Geometric Measure Theory Approach to Exterior Problems for Minimal Surfaces (pdf 558.26 KB)
Michael Gruter
9 - Singularity Formation in Geometric Evolution Equations (pdf 915.57 KB)
Gerhard Huisken
10 - Computing Conformal Maps and Minimal Surfaces (pdf 2.57 MB)
John Hutchinson
11 - Second Order Elliptica Equations with Venttsel Boundary Conditions (pdf 751.39 KB)
Yousong Luo
12 - Variational Properties of Some Simple Boundary Integral Equations (pdf 1.28 MB)
W McLean
13 - Some Topical Variational Geometry Problems in Computer Graphics (pdf 1.98 MB)
GN Newsam
14 - Local Spline Approximants (pdf 647.86 KB)
Andrew H Norton
15 - New Periodic Minimal Surfaces in H3 (pdf 1.22 MB)
Konrad Polthier
16 - Hierarchical N-Body Calculations (pdf 1.24 MB)
Stephen Roberts
17 - Solution Geometry, KAC-MOODY Algerbras and the Yang-Baxter Equations (pdf 822.72 KB)
Ivan Sterling
18 - Crystalline Geometric Crystal growth (pdf 385.8 KB)
Jean E Taylor
19 - Further Existence Results for Two Point Boundary Value Problems Arising in Electro-Diffusion (pdf 535.11 KB)
HB Thompson
20 - Plateau's Problem for Minimal Surface with a Catenoidal End (pdf 837.17 KB)
Friedrich Tomi
21 - Boundary Regularity for the Solution of the Equation of Prescribed Mean Curvature (pdf 398.06 KB)
John IE Urbas
22 - Least Gradient Problems (pdf 901.6 KB)
Graham Williams
23 - Compensated Compactness and the Biting Lemma (pdf 586.58 KB)
Lewei Zhang