Abstract.
A ring type spanner in a wedge is a compact embedded annular surface of constant mean curvature which meets the planes of the wedge in constant angles along its boundary. In this paper we show that every ring type spanner in a wedge is spherical.
Similar content being viewed by others
References
Alexandrov, A.D.: Uniqueness theorems for surfaces in the large. V. Vestnik Leningrad Univ. 13, A.M.S. (series 2), 21, 412–416 (1958)
Burago, Y., Zalgaller, V.: Geometric inequalities. Springer, Berlin, 1988
do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, New Jersey, 1976
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Springer, Berlin, 2001
Hopf, H.: Differential Geometry in the large. Springer, Berlin, 1989
Lawson, H.B. Jr.: Lectures on minimal submanifolds. Publish or Perish, Berkeley, 1980
McCuan, J.: Symmetry via spherical reflection and spanning drops in a wedge. PhD Thesis, Stanford, 1995
McCuan, J.: Symmetry via spherical reflection and spanning drops in a wedge. Pacific J. Math. 180, 291–323 (1997)
McCuan, J.: Symmetry via spherical reflection. J. Geom. Anal. 10, 545–564 (2000)
Sauvigny, F.: On immersions of constant mean curvature: compactness results and finiteness theorems for Plateau’s problem. Arch. Rational Mech. Anal. 110, 125–140 (1990)
Schoen, R.: Uniqueness, symmetry, and embeddedness of minimal surfaces. J. Differential Geometry 18, 791–809 (1983)
Serrin, J.: A symmetry problem in potential theory. Arch. Rat. Mech. and Anal. 43, 304–318 (1971)
Wente, H.C.: The symmetry of sessile and pendent drops. Pacific J. Math. 88, 387–397 (1980)
Wente, H.C.: Tubular capillary surfaces in a convex body. Advances in geometric analysis and continuum mechanics (Stanford, CA, 1993), 288–298, International Press, Cambridge, MA, 1995
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Park, Sh. Every ring type spanner in a wedge is spherical. Math. Ann. 332, 475–482 (2005). https://doi.org/10.1007/s00208-005-0476-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-005-0476-2