Hiroshima Mathematical Journal

Kuramochi boundaries of infinite networks and extremal problems

Atsushi Murakami

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 24, Number 2 (1994), 243-256.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206128024

Digital Object Identifier
doi:10.32917/hmj/1206128024

Mathematical Reviews number (MathSciNet)
MR1284375

Zentralblatt MATH identifier
0815.31005

Subjects
Primary: 31C45: Other generalizations (nonlinear potential theory, etc.)
Secondary: 30F25: Ideal boundary theory 90C35: Programming involving graphs or networks [See also 90C27]

Citation

Murakami, Atsushi. Kuramochi boundaries of infinite networks and extremal problems. Hiroshima Math. J. 24 (1994), no. 2, 243--256. doi:10.32917/hmj/1206128024. https://projecteuclid.org/euclid.hmj/1206128024


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References

  • [1] R. J. Duffin, Discrete potential theory, Duke Math. J., 20 (1953), 233-251.
  • [2] T. Fuji'i'e, Extremal length and Kuramochi boundary, J. Math. Kyoto Univ., 4 (1964), 149-159.
  • [3] T. Kayano and M.Yamasaki, Boundary limit of discrete Dirichlet potentials, Hiroshima Math. J., 14 (1984), 401-406.
  • [4] A. Murakami and M.Yamasaki, Extremal problems with respect to ideal boundary components of an infinite network, Hiroshima Math. J., 19 (1989), 77-87.
  • [5] T. Nakamura and M.Yamasaki, Generalized extremal length of an infinite network, Hiroshima Math. J., 6 (1976), 95-111.
  • [6] M.Ohtsuka, An elementary introduction of Kuramochi boundary, J. Sci. Hiroshima Univ., Ser. A-I Math., 28 (1964), 271-299.
  • [7] M.Ohtsuka, Dirichlet principle on Riemann surfaces, J. Analyse Math., 19 (1967), 295-311.
  • [8] M.Yamasaki, Extremum problems on an infinite network, Hiroshima Math. J., 5 (1975), 223-250.
  • [9] M.Yamasaki, Discrete potentials on an infinite network, Mem. Fac.Sci. Shimane Univ., 13 (1979), 31-44.
  • [10] M.Yamasaki, Ideal boundary limit of discrete Dirichlet functions, Hiroshima Math. J., 16 (1986), 353-360.