On the existence of minimal surfaces with singular boundaries
HTML articles powered by AMS MathViewer
- by Howard Iseri
- Proc. Amer. Math. Soc. 124 (1996), 3493-3500
- DOI: https://doi.org/10.1090/S0002-9939-96-03585-X
- PDF | 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
- Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
- Joel Hass, Singular curves and the Plateau problem, Internat. J. Math. 2 (1991), no. 1, 1–16. MR 1082833, DOI 10.1142/S0129167X91000028
- H. Blaine Lawson Jr., Lectures on minimal submanifolds. Vol. I, Monografías de Matemática [Mathematical Monographs], vol. 14, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1977. MR 527121
- Friedrich Tomi and Anthony J. Tromba, Existence theorems for minimal surfaces of nonzero genus spanning a contour, Mem. Amer. Math. Soc. 71 (1988), no. 382, iv+83. MR 920962, DOI 10.1090/memo/0382
Bibliographic 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