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Lower bound for the area of an analytic curve inside a cube in the space ℂn

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Abstract

The exact lower bound of the area of an analytic curve which lies inside a cube in the space ℂ and passes through its center is obtained.

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References

  1. P. Lelong and L. Grumman,Integer Functions of Many Complex Variables [Russian translation], Mir, Moscow, (1989).

    Google Scholar 

  2. H. Aleksander and R. Osserman, “Area bounds for various classes of surfaces,”Amer. J. Math.,97, 753–769 (1975).

    Google Scholar 

  3. J. Korevaar, J. Wiegerinck, and R. Zeinstra, “Minimal area of zero sets in tube domains of ℂ,”Proc. Kon. Ned. Akad. van Wetensch. A.87, 283–290 (1984).

    Google Scholar 

  4. R. Zeinstra, “On a question concerning zero sets of minimal area in domains of ℂ,”Proc. Kon. Ned. Akad. van Wetensch. A.,87, 291–297 (1984).

    Google Scholar 

  5. B. Z. Katsnel'son and L. I. Ronkin, “On minimal volume of an analytical set,”Sib. Mat. Zh.,15, No 3, 516–528 (1974).

    Google Scholar 

  6. Y. Nikityuk, “On one problem of integral geometry,”Teor. Func., Func. Anal. Pril., Issue 53, 95–99 (1990).

  7. M. Erve,Functions of Many Complex Variables (Local Theory), [Russian translation], Mir, Moscow, (1965).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 145–148, January, 1993.

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Ronkin, L.I. Lower bound for the area of an analytic curve inside a cube in the space ℂn . Ukr Math J 45, 162–164 (1993). https://doi.org/10.1007/BF01062052

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  • DOI: https://doi.org/10.1007/BF01062052

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