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An inequality between the exterior diameter and the mean curvature of bounded immersions

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References

  1. Aminov, Ju: The exterior diameter of an immersed Riemannian manifold. Mat. Sb.92 (134), 456–460 (1973) [Russian]. Engl. Transl.: Math. USSR-Sb.21, 449–454 (1973)

    Google Scholar 

  2. Chern, S.: The geometry ofG-structures. Bull. Amer. Math. Soc.72 (1966)

  3. Hasanis, Th.: Isometric immersions into spheres. J. Math. Soc. Japan (to appear)

  4. Hasanis, Th., Koutroubiotis, D.: Immersions of bounded mean curvature. Arch. Math. (Basel)33, 170–171 (1979) and “Addendum” (to appear)

    Google Scholar 

  5. Hasanis, Th., Koutroubiotis, D.: Addendum to [4]

  6. Hoffman, K.: Banach spaces of Analytic functions. Englewood Cliffs, New Jersey: Prentice-Hall 1962

    Google Scholar 

  7. Jones, P.: A complete bounded complex submanifold of ℂ3. Proc. Amer. Math. Soc.76, 305–306 (1979)

    Google Scholar 

  8. Jorge, L., Koutroubiotis, D.: An estimate for the curvature of bounded submanifolds. Preprint

  9. Jorge, L., Xavier, F.: On the existence of complete bounded minimal surfaces. Bol. Soc. Brasil. Mat.10, No 2 (1979)

    Google Scholar 

  10. Jorge, L., Xavier, F.: A complete minimal surface in ℝ3 between two paralel planes. Ann. of Math. (to appear)

  11. Omori, H.: Isometric immersions of Riemannian manifolds. J. Math. Soc. Japan19, 205–214 (1967)

    Google Scholar 

  12. Ossermann, R.: A survey of minimal surfaces. New York-Toronto-London: Van Nostrand Reinhold 1969

    Google Scholar 

  13. Wu, H.: On a problem concerning the intrinsic characterization of ℂn. Math. Ann.246, 15–22 (1979)

    Google Scholar 

  14. Zygmund, A.: Trigonometric series (vol. II). Cambridge: At the University Press 1968

    Google Scholar 

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Jorge, L.P.d.M., Xavier, F.V. An inequality between the exterior diameter and the mean curvature of bounded immersions. Math Z 178, 77–82 (1981). https://doi.org/10.1007/BF01218372

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