Computing least area hypersurfaces spanning arbitrary boundaries Academic Article

abstract

• The numerical least area problem for oriented hypersurfaces seeks algorithms which approximate area-minimizing hypersurfaces spanning a given boundary in Euclidean n-dimensional space. A mathematical model and numerical implementation are presented for finding the solution to the general least area problem for oriented surfaces in Euclidean three-dimensional space. (The mathematical model is valid for hypersurfaces of arbitrary Euclidean n-dimensional spaces.) There are no a priori restrictions on either the topological complexity of the given boundary or the topological type of the surfaces considered. As an example which illustrates the power of the method, the algorithm is applied to a boundary consisting of a pair of square-shaped linked curves. The resulting numerical surface is compared with an actual physical area-minimizing spanning surface (soap film).

authors

• Pitts, Jon

published proceedings

• SIAM JOURNAL ON SCIENTIFIC COMPUTING

author list (cited authors)

• Parks, H. R., & Pitts, J. T.

citation count

• 9

complete list of authors

• Parks, HR||Pitts, JT

publication date

• May 1997

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Scientific Computing  Journal

keywords

• Area-minimizing Currents
• Area-minimizing Surfaces
• Functions Of Least Gradient
• Method Of Least Gradient

Digital Object Identifier (DOI)

• 10.1137/S1064827594278903

start page

• 886

end page

• 917

volume

• 18

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1137%2Fs1064827594278903