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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the existence of minimal surfaces with singular boundaries
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by Howard Iseri PDF
Proc. Amer. Math. Soc. 124 (1996), 3493-3500 Request permission

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.
References
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Additional Information
  • Howard Iseri
  • Affiliation: Department of Mathematics and Computer Information Science, Mansfield University, Mansfield, Pennsylvania 16933
  • Email: hiseri@.mnsfld.edu
  • 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
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 3493-3500
  • MSC (1991): Primary 53A10, 49Q05
  • DOI: https://doi.org/10.1090/S0002-9939-96-03585-X
  • MathSciNet review: 1350948