Extremal metrics and modulus

I. Anić; M. Mateljević; Dragomir Šarić

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 2, page 225-235
  • ISSN: 0011-4642

Abstract

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We give a new proof of Beurling’s result related to the equality of the extremal length and the Dirichlet integral of solution of a mixed Dirichlet-Neuman problem. Our approach is influenced by Gehring’s work in ℝ 3 space. Also, some generalizations of Gehring’s result are presented.

How to cite

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Anić, I., Mateljević, M., and Šarić, Dragomir. "Extremal metrics and modulus." Czechoslovak Mathematical Journal 52.2 (2002): 225-235. <http://eudml.org/doc/30695>.

@article{Anić2002,
abstract = {We give a new proof of Beurling’s result related to the equality of the extremal length and the Dirichlet integral of solution of a mixed Dirichlet-Neuman problem. Our approach is influenced by Gehring’s work in $\mathbb \{R\}^3$ space. Also, some generalizations of Gehring’s result are presented.},
author = {Anić, I., Mateljević, M., Šarić, Dragomir},
journal = {Czechoslovak Mathematical Journal},
keywords = {extremal distance; conformal capacity; Beurling theorem; extremal distance; conformal capacity; Beurling theorem},
language = {eng},
number = {2},
pages = {225-235},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extremal metrics and modulus},
url = {http://eudml.org/doc/30695},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Anić, I.
AU - Mateljević, M.
AU - Šarić, Dragomir
TI - Extremal metrics and modulus
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 225
EP - 235
AB - We give a new proof of Beurling’s result related to the equality of the extremal length and the Dirichlet integral of solution of a mixed Dirichlet-Neuman problem. Our approach is influenced by Gehring’s work in $\mathbb {R}^3$ space. Also, some generalizations of Gehring’s result are presented.
LA - eng
KW - extremal distance; conformal capacity; Beurling theorem; extremal distance; conformal capacity; Beurling theorem
UR - http://eudml.org/doc/30695
ER -

References

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  2. 10.1090/S0002-9947-1962-0139735-8, Trans. Amer. Math. Soc. 103 (1962), 383–393. (1962) Zbl0113.05805MR0139735DOI10.1090/S0002-9947-1962-0139735-8
  3. 10.1090/S0002-9904-1963-10902-7, Bull. Amer. Math. Soc. 69 (1963). (1963) Zbl0136.38102MR0145071DOI10.1090/S0002-9904-1963-10902-7
  4. 10.1307/mmj/1029000164, Michigan Math. J. 16 (1969), 43–51. (1969) MR0247077DOI10.1307/mmj/1029000164
  5. Quadratic Differentials, Springer-Verlag, 1984. (1984) Zbl0547.30038MR0743423
  6. Dirichlet’s Principle, Conformal Mappings and Minimal Surfaces, New York, Interscience Publishers, Inc., 1950. (1950) MR0036317
  7. Teichmüller Theory and Quadratic Differentials, New York, A Wiley-Interscience Publication, 1987. (1987) Zbl0629.30002MR0903027
  8. Differential Geometry: Manifolds, Curves and Surfaces, Springer-Verlag, 1987. (1987) MR0903026
  9. On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. A 298 (1961), 1–36. (1961) Zbl0096.27506MR0140685
  10. On the conformal capacity in space, J. Math. Mech. 8 (1959), 411–414. (1959) Zbl0086.28203MR0104785

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