[KSCI] Korea Science Citation Index Service

JIN, Sun-Sook (Major in Mathematics and Applies Mathematics College of Electronics and Information Kyung Hee University)

Publication Information

Abstract

In this article, we prove the existence of a minimal annulus bounded by a Jordan curve and a straight line.

Keywords

Douglas-Plateau problem; minimal surfaces; Riemann's minimal examples; Courant-Lebesgue lemma;

Citations & Related Records

1	J. Douglas,The problem of Plateau for two contours, J. Math. Phys. Massachusetts Inst. of Tech. 10 (1930/31), 315-359
2	Yi Fang, On minimal annuli in a slab, Comm. Math. Helv. 69 (1994), 417-430 DOI
3	Yi Fang and Jenn-Fang Hwang, Curvature estimates for minimal annuli and noncompact Douglas-Plateau problem, Comm. Anal. Geom. 8 (2000), no. 4, 871-904 DOI
4	H. Jenkins and J. Serrin, Variational problems of minimal surface type, 2, Boundary value problems for the minimal surface equation, Arch. Rational Mech. Anal. 21 (1966),321-342
5	F. J. Lopez and F. Wei, Properly immersed minimal discs bounded by straight lines, Math. Ann. 318 (2000), 667-706 DOI ScienceOn
6	J. Perez and A. Ros, Properly embedded minimal annuli bounded by a convex curve, Journal de l'Institut Mathematique de Jussieu 1 (2002), no. 2, 293-305 DOI
7	B. Riemann, Uber die Fliiche vom kleinsten Inhalt bei gegebener Begrebzung, Abh. Konigl, d. Wiss. Gottingen, Mathern. Cl. 13 (1867), 3-52
8	. Tomi and R. Ye, The exterior plateau problem, Math. Z. 205 (1990), 233-245 DOI
9	R. Courant, Dirichlet's principle, conformal mapping and minimal surfaces, New York, Interscience, 1950
10	U. Dierkes, S. Hildebrandt, A. Kuster, and O. Wohlrab, Minimal Surfaces 1, Springer-Verlag, 1992
11	J. Douglas, Solution to the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931), 263-321 DOI ScienceOn