Skip to main content
Log in

Every ring type spanner in a wedge is spherical

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alexandrov, A.D.: Uniqueness theorems for surfaces in the large. V. Vestnik Leningrad Univ. 13, A.M.S. (series 2), 21, 412–416 (1958)

  2. Burago, Y., Zalgaller, V.: Geometric inequalities. Springer, Berlin, 1988

  3. do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, New Jersey, 1976

  4. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Springer, Berlin, 2001

  5. Hopf, H.: Differential Geometry in the large. Springer, Berlin, 1989

  6. Lawson, H.B. Jr.: Lectures on minimal submanifolds. Publish or Perish, Berkeley, 1980

  7. McCuan, J.: Symmetry via spherical reflection and spanning drops in a wedge. PhD Thesis, Stanford, 1995

  8. McCuan, J.: Symmetry via spherical reflection and spanning drops in a wedge. Pacific J. Math. 180, 291–323 (1997)

    Google Scholar 

  9. McCuan, J.: Symmetry via spherical reflection. J. Geom. Anal. 10, 545–564 (2000)

    Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Schoen, R.: Uniqueness, symmetry, and embeddedness of minimal surfaces. J. Differential Geometry 18, 791–809 (1983)

    Google Scholar 

  12. Serrin, J.: A symmetry problem in potential theory. Arch. Rat. Mech. and Anal. 43, 304–318 (1971)

    Google Scholar 

  13. Wente, H.C.: The symmetry of sessile and pendent drops. Pacific J. Math. 88, 387–397 (1980)

    Google Scholar 

  14. 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

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sung-ho Park.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-005-0476-2

Keywords

Navigation