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Proceedings of the American Mathematical Society

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On the existence of minimal
surfaces with singular boundaries

Author: Howard Iseri
Journal: Proc. Amer. Math. Soc. 124 (1996), 3493-3500
MSC (1991): Primary 53A10, 49Q05
MathSciNet review: 1350948
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Abstract: In 1931, Jesse Douglas showed that in $ \mathbb {R}^{n}$, every set of $k$ rectifiable Jordan curves, with $k \ge 2$, 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.

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Howard Iseri
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

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