Open book structures and unicity of minimal submanifolds

R. Hardt; Harold Rosenberg

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 3, page 701-708
  • ISSN: 0373-0956

Abstract

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We prove unicity of certain minimal submanifolds, for example Clifford annuli in S 3 . The idea is to consider the placement of the submanifold with respect to the (singular) foliation of S 3 by the Clifford annuli whose boundary are two fixed great circles a distance π / 2 apart.

How to cite

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Hardt, R., and Rosenberg, Harold. "Open book structures and unicity of minimal submanifolds." Annales de l'institut Fourier 40.3 (1990): 701-708. <http://eudml.org/doc/74893>.

@article{Hardt1990,
abstract = {We prove unicity of certain minimal submanifolds, for example Clifford annuli in $S^3$. The idea is to consider the placement of the submanifold with respect to the (singular) foliation of $S^3$ by the Clifford annuli whose boundary are two fixed great circles a distance $\pi /2$ apart.},
author = {Hardt, R., Rosenberg, Harold},
journal = {Annales de l'institut Fourier},
keywords = {minimal submanifolds; Clifford annuli},
language = {eng},
number = {3},
pages = {701-708},
publisher = {Association des Annales de l'Institut Fourier},
title = {Open book structures and unicity of minimal submanifolds},
url = {http://eudml.org/doc/74893},
volume = {40},
year = {1990},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 3
SP - 701
EP - 708
AB - We prove unicity of certain minimal submanifolds, for example Clifford annuli in $S^3$. The idea is to consider the placement of the submanifold with respect to the (singular) foliation of $S^3$ by the Clifford annuli whose boundary are two fixed great circles a distance $\pi /2$ apart.
LA - eng
KW - minimal submanifolds; Clifford annuli
UR - http://eudml.org/doc/74893
ER -

References

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  1. [GT] D. GILBARG & N. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0361.35003MR57 #13109
  2. [H] J. HASS, Minimal surfaces in foliated manifolds, Comm. Math. Helv., 61 n°1 (1986), 1-32. Zbl0601.53024MR88d:53006
  3. [HS] R. HARDT & L. SIMON, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math., 110 (1979), 439-486. Zbl0457.49029MR81i:49031
  4. [L] H.B. LAWSON, Complete minimal surfaces in Sn, Ann. of Math., 92 (1970), 335-374. Zbl0205.52001MR42 #5170
  5. [M] F. MORGAN, On finiteness of the number of stable minimal hypersurfaces with a fixed boundary, Indiana U. Math. J., 35 (1986), 779-833. Zbl0592.53004MR88b:49059
  6. [Sh] M. SHIFFMAN, On surfaces of stationary bounded by two circles, or convex curves, in parallel planes, Ann. of Math., 3 (1956), 77-90. Zbl0070.16803MR17,632d
  7. [So] B. SOLOMON, On the Gauss map of an area-minimizing hypersurface, J. Diff. Geom., 24 (1984), 221-232. Zbl0548.53051MR86e:49079

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