On the existence of minimal
surfaces with singular boundaries
Abstract: In 1931, Jesse Douglas showed that in , every set of rectifiable Jordan curves, with , bounds an area-minimizing minimal surface with prescribed topological type if a ``condition of cohesion'' is satisfied. In this paper, it is established that under similar conditions, this result can be extended to non-Jordan curves.
Affiliation: Department of Mathematics and Computer Information Science, Mansfield University, Mansfield, Pennsylvania 16933
Keywords: Plateau's problem, minimal surfaces, singular boundary curves, Douglas condition, condition of cohesion, condition of adhesion
Received by editor(s): May 9, 1995
Additional Notes: This work was begun as a graduate student at the University of California, Davis, under the continuing guidance of Professor Joel Hass.
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society