Near-stability of a quasi-minimal surface indicated through a tested curvature algorithm

• Published in: Computers & mathematics with applications (1987) Vol. 69; no. 10; pp. 1242 - 1262
• Main Authors: Ahmad, Daud, Masud, Bilal
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-05-2015
• Subjects: Algorithms; Bilinear interpolation; Boundaries; Curvature; Curvature algorithm; Mathematical analysis; Mathematical models; Minimal surfaces; Stability; Straight lines; Variational improvement; Curvature algorithm; Variational improvement; Minimal surfaces; Bilinear interpolation
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2015.03.015

We decrease the rms mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately chosen non-minimal surface, we achieve up to 65 percent of the total possible decrease in area. When we apply our algorithm to a bilinear interpolant bounded by four non-coplanar straight lines, the area decrease by the same algorithm is only 0.116179 percent of the original value. This relative stability suggests that the bilinear interpolant is already a quasi-minimal surface.