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The Hahn metric on Riemann surfaces. (English) Zbl 0524.30013


MSC:

30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
32F45 Invariant metrics and pseudodistances in several complex variables
30F99 Riemann surfaces
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
53B35 Local differential geometry of Hermitian and Kählerian structures

Citations:

Zbl 0476.32031
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Full Text: DOI

References:

[1] C. CARATHEODORY, Theory of Functions, Vol. II, 2nd ed., Chelsea Publ. Co., New York, I960. · JFM 42.0275.03
[2] E. T. COPSON, An Introduction to the Theory of Functions of a Complex Variable, Oxford Univ. Press, London, 1935. · Zbl 0012.16902
[3] H. M. FARKAS AND I. KRA, Riemann Surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York, 1980. · Zbl 0475.30001
[4] K. T. HAHN, Some remarks on a new pseudo-differential metric, Ann. Polon. Math. 39 (1981), 71-81. · Zbl 0476.32031
[5] W. K. HAYMAN, Multivalent Functions, Cambridge Tracts in Mathematics and Mathematical Physics, no. 48, Cambridge Univ. Press, 1967. · Zbl 0082.06102
[6] M. HEINS, On a class of conformal metrics, Nagoya Math. J. 21 (1962), 1-60. · Zbl 0113.05603
[7] J. A. JENKINS, On the existence of certain general extremal metrics, Ann. of Math. 66 (1957), 440-453. · Zbl 0082.06301 · doi:10.2307/1969901
[8] J. A. JENKINS AND N. SUITA, On the representation and compactifcation of Riemann surfaces, Bull. Inst. Math. Acad. Sinica 6 (1978), 423-427. · Zbl 0401.30038
[9] J. LEHNER, A Short Course in Automorphic Functions, Holt, Rinehart and Winston, New York, 1966. · Zbl 0138.31404
[10] G. MORETTI, Functions of a Complex Variable, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
[11] Z. NEHARI, Conformal Mapping, McGraw-Hill, New York, 1952. · Zbl 0048.31503
[12] K. STREBEL, On quadratic differentials with closed trajectories and second order poles, J. Analyse Math. 19 (1967), 373-382. · Zbl 0158.32402 · doi:10.1007/BF02788726
[13] N. SUITA, On a metric induced by analytic capacity, Kdai Math. Sem. Rep. 25 (1973), 215-218. · Zbl 0264.30023 · doi:10.2996/kmj/1138846773
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