Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON THE SYMMETRY OF ANNULAR BRYANT SURFACE WITH CONSTANT CONTACT ANGLE

  • Park, Sung-Ho (Major in Mathematics Graduate School of Education Hankuk University of Foreign Studies)
  • Received : 2013.11.12
  • Accepted : 2014.03.17
  • Published : 2014.03.30
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Abstract

We show that a compact immersed annular Bryant surface in $\mathbb{H}^3$ meeting two parallel horospheres in constant contact an gles is rotational.

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References

  1. A. D. Alexandrov, Uniqueness theorems for surfaces in the large V, Amer. Math. Soc. Transl. 21 (1962), 412-416.
  2. R. Bryant, Surfaces with constant mean curvature one in hyperbolic space, Asterisque 154-155: 321-347.
  3. Y. Fang, Lectures on minimal surfaces in ${\mathbb{R}}^3$, Center for Mathematics and Its applications, Australian National University, (1996).
  4. H. Hopf, Differential Geometry in the large, Springer, Berlin, (1989).
  5. H. B. Lawson, Complete Minimal Surfaces in ${\mathbb{S}}^3$, Ann. of Math. 2nd Ser. 92 (3) (1970), 335-374. https://doi.org/10.2307/1970625
  6. L. Lima and P. Roitman, Constant mean curvature one surfaces in hyperbolic space using Bianchi-Calo method, Annals of the Braz. Acad. of Sci. 74 (2002) (1), 19-24; arXiv:math/0110021. https://doi.org/10.1590/S0001-37652002000100002
  7. J. McCuan, Symmetry via spherical reflection and spanning drops in a wedge, Pacific J. Math. 180 (1997) (2), 291-323. https://doi.org/10.2140/pjm.1997.180.291
  8. J. C. C. Nitsche, Stationary partitioning of convex bodies, Arch. Rat. Mech. Anal. 89 (1985), 1-19. https://doi.org/10.1007/BF00281743
  9. J. Pyo, Minimal annuli with constant contact angle along the planar boundaries, Geom. Dedicata 146 (1) (2010), 159-164. https://doi.org/10.1007/s10711-009-9431-9
  10. W. Rossman and K. Sato, Constant mean curvature surfaces with two ends in hyperbolic space, Experiment. Math. Volume 7, Issue 2 (1998), 101-119. https://doi.org/10.1080/10586458.1998.10504360
  11. J. Serrin, A symmetry problem in potential theory, Arch. Rat. Mech. and Anal. 43 (1971), 304-318.
  12. H. Wente, Tubular capillary surfaces in a convex body. Advances in geometric analysis and continuum mechanics (Stanford, CA, 1993), 288-298, International Press, Cambridge, MA, (1995).