Korean J. Math. Vol. 22 No. 1 (2014) pp.133-138
DOI: https://doi.org/10.11568/kjm.2014.22.1.133

On the symmetry of annular Bryant surface with constant contact angle

Main Article Content

Sungho Park

Abstract

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


Article Details

Supporting Agencies

Sung-Ho Park Hankuk University of Foreign Studies Graduate School of Education Major in Mathematics

References

[1] A. D. Alexandrov, Uniqueness theorems for surfaces in the large V, Amer. Math. Soc. Transl. 21 (1962), 412–416. Google Scholar

[2] R. Bryant, Surfaces with constant mean curvature one in hyperbolic space, Ast erisque 154-155: 321-347. Google Scholar

[3] Y. Fang, Lectures on minimal surfaces in R3, Center for Mathematics and Its applications, Australian National University, (1996). Google Scholar

[4] H. Hopf, Differential Geometry in the large, Springer, Berlin, (1989). Google Scholar

[5] H. B. Lawson, Complete Minimal Surfaces in S3, Ann. of Math. 2nd Ser. 92 (3) (1970), 335–374. Google Scholar

[6] L. Lima and P. Roitman, Constant mean curvature one surfaces in hyperbolic space using Bianchi-Cal`o method, Annals of the Braz. Acad. of Sci. 74 (2002) (1), 19–24; arXiv:math/0110021. Google Scholar

[7] J. McCuan, Symmetry via spherical reflection and spanning drops in a wedge, Pacific J. Math. 180 (1997) (2), 291–323. Google Scholar

[8] J. C. C. Nitsche, Stationary partitioning of convex bodies, Arch. Rat. Mech. Anal. 89 (1985), 1–19. Google Scholar

[9] J. Pyo, Minimal annuli with constant contact angle along the planar boundaries, Geom. Dedicata 146 (1) (2010), 159–164. Google Scholar

[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. Google Scholar

[11] J. Serrin, A symmetry problem in potential theory, Arch. Rat. Mech. and Anal. 43 (1971), 304–318. Google Scholar

[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). Google Scholar