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Minimal annuli with constant contact angle along the planar boundaries

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Abstract

We show that an immersed minimal annulus, with two planar boundary curves along which the surface meets these planes with constant contact angle, is part of the catenoid.

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References

  1. Cheng S., Tysk J.: An index characterization of the catenoid and index bounds for minimal surfaces in R 4. Pac. J. Math. 134, 251–260 (1988)

    MATH  MathSciNet  Google Scholar 

  2. Choe J.: Sufficient conditions for constant mean curvature surfaces to be round. Math. Ann. 323, 143–156 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Collin P.: Topologie et courbure des surfaces minimales proprement plongees de \({\mathbb{R}^3}\). Ann. Math. 145(2), 1–31 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dierkes U., Hildebrandt S., Kuster A., Wohlrab O.: Minimal Surfaces I, Grundlehren Math. Wiss. 295. Springer, Berlin (1992)

    Google Scholar 

  5. Ekholm T., White B., Wienholtz D.: Embeddedness of minimal surfaces with total boundary curvature at most 4π. Ann. Math. 155(2), 209–234 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hopf H.: Differential Geometry in the Large. Lecture Notes Math 1000. Springer, Berlin (1989)

    Google Scholar 

  7. López F., Ros A.: On embedded complete minimal surfaces of genus zero. J. Differ. Geom. 33, 293–300 (1991)

    MATH  Google Scholar 

  8. Nitsche J.C.C.: A characterization of the catenoid. J. Math. Mech. 11, 293–301 (1962)

    MATH  MathSciNet  Google Scholar 

  9. Nitsche J.C.C.: Lectures on Minimal Surfaces, Vol. 1. Combridge University Press, Combridge (1989)

    Google Scholar 

  10. Osserman R.: Global properties of minimal surfaces in E 3 and E n. Ann. Math. 80(2), 340–364 (1964)

    Article  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Shiffman M.: On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes. Ann. Math. 63(2), 77–90 (1956)

    Article  MathSciNet  Google Scholar 

  14. Souam R.: Schiffer’s problem and an isoperimetric inequality for the first buckling eigenvalue of domains on \({\mathbb{S}^2}\). Ann. Global Anal. Geom. 27, 341–354 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Spivak M.: A Comprehensive Introduction to Differential Geometry, Vol. III. Publish or Perish, Berkeley (1979)

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  17. Wente H.: Tubular capillary surfaces in a convex body. In: Concus, P., Lancaster, K. (eds) Advances in Geometric Analysis and Continuum Mechanics, pp. 288–298. International Press, London (1995)

    Google Scholar 

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Correspondence to Juncheol Pyo.

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Pyo, J. Minimal annuli with constant contact angle along the planar boundaries. Geom Dedicata 146, 159–164 (2010). https://doi.org/10.1007/s10711-009-9431-9

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  • DOI: https://doi.org/10.1007/s10711-009-9431-9

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