We prove unicity of certain minimal submanifolds, for example Clifford annuli in . The idea is to consider the placement of the submanifold with respect to the (singular) foliation of by the Clifford annuli whose boundary are two fixed great circles a distance apart.
Nous démontrons l’unicité de certaines sous-variétés minimales, par exemple, les anneaux de Clifford dans . L’idée est de regarder le placement de la sous-variété minimale par rapport au feuilletage singulier de par des anneaux de Clifford de bord deux géodésiques fixées à une distance .
@article{AIF_1990__40_3_701_0,
author = {Hardt, R. and Rosenberg, Harold},
title = {Open book structures and unicity of minimal submanifolds},
journal = {Annales de l'Institut Fourier},
pages = {701--708},
year = {1990},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {40},
number = {3},
doi = {10.5802/aif.1229},
zbl = {0702.53039},
mrnumber = {92e:53009},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1229/}
}
TY - JOUR AU - Hardt, R. AU - Rosenberg, Harold TI - Open book structures and unicity of minimal submanifolds JO - Annales de l'Institut Fourier PY - 1990 SP - 701 EP - 708 VL - 40 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1229/ DO - 10.5802/aif.1229 LA - en ID - AIF_1990__40_3_701_0 ER -
%0 Journal Article %A Hardt, R. %A Rosenberg, Harold %T Open book structures and unicity of minimal submanifolds %J Annales de l'Institut Fourier %D 1990 %P 701-708 %V 40 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1229/ %R 10.5802/aif.1229 %G en %F AIF_1990__40_3_701_0
Hardt, R.; Rosenberg, Harold. Open book structures and unicity of minimal submanifolds. Annales de l'Institut Fourier, Tome 40 (1990) no. 3, pp. 701-708. doi: 10.5802/aif.1229
[GT] & , Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg-New York, 1977. | Zbl | MR
[H] , Minimal surfaces in foliated manifolds, Comm. Math. Helv., 61 n°1 (1986), 1-32. | Zbl | MR
[HS] & , Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math., 110 (1979), 439-486. | Zbl | MR
[L] , Complete minimal surfaces in Sn, Ann. of Math., 92 (1970), 335-374. | Zbl | MR
[M] , On finiteness of the number of stable minimal hypersurfaces with a fixed boundary, Indiana U. Math. J., 35 (1986), 779-833. | Zbl | MR
[Sh] , On surfaces of stationary bounded by two circles, or convex curves, in parallel planes, Ann. of Math., 3 (1956), 77-90. | Zbl | MR
[So] , On the Gauss map of an area-minimizing hypersurface, J. Diff. Geom., 24 (1984), 221-232. | Zbl | MR
Cité par Sources :



