| Title:
|
Extremal metrics and modulus (English) |
| Author:
|
Anić, I. |
| Author:
|
Mateljević, M. |
| Author:
|
Šarić, D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
225-235 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
extremal distance |
| Keyword:
|
conformal capacity |
| Keyword:
|
Beurling theorem |
| MSC:
|
30A15 |
| MSC:
|
30C85 |
| idZBL:
|
Zbl 1014.30015 |
| idMR:
|
MR1905432 |
| . |
| Date available:
|
2009-09-24T10:50:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127713 |
| . |
| Reference:
|
[ahl] L. V. Ahlfors: Conformal Invariants.McGraw-Hill Book Company, 1973. Zbl 0272.30012, MR 0357743 |
| Reference:
|
[geh1] F. W. Gehring: Rings and quasiconformal mappings in space.Trans. Amer. Math. Soc. 103 (1962), 383–393. Zbl 0113.05805, MR 0139735, 10.1090/S0002-9947-1962-0139735-8 |
| Reference:
|
[geh3] F. W. Gehring: Quasiconformal mappings in space.Bull. Amer. Math. Soc. 69 (1963). Zbl 0136.38102, MR 0145071, 10.1090/S0002-9904-1963-10902-7 |
| Reference:
|
[zie] W. P. Ziemer: Extremal lenght and $p$-capacity.Michigan Math. J. 16 (1969), 43–51. MR 0247077, 10.1307/mmj/1029000164 |
| Reference:
|
[streb] K. Strebel: Quadratic Differentials.Springer-Verlag, 1984. Zbl 0547.30038, MR 0743423 |
| Reference:
|
[cour] R. Courant: Dirichlet’s Principle, Conformal Mappings and Minimal Surfaces.New York, Interscience Publishers, Inc., 1950. MR 0036317 |
| Reference:
|
[gar] F. P. Gardiner: Teichmüller Theory and Quadratic Differentials.New York, A Wiley-Interscience Publication, 1987. Zbl 0629.30002, MR 0903027 |
| Reference:
|
[tub] M. Berger, B. Gostiaux: Differential Geometry: Manifolds, Curves and Surfaces.Springer-Verlag, 1987. MR 0903026 |
| Reference:
|
[vai] J.Väisälä: On quasiconformal mappings in space.Ann. Acad. Sci. Fenn. Ser. A 298 (1961), 1–36. Zbl 0096.27506, MR 0140685 |
| Reference:
|
[low] C. Loewner: On the conformal capacity in space.J. Math. Mech. 8 (1959), 411–414. Zbl 0086.28203, MR 0104785 |
| . |
