| Title:
|
Estimates for the energy integral of quasiregular mappings on Riemannian manifolds and isoperimetry (English) |
| Author:
|
Martio, O. |
| Author:
|
Miklyukov, V. |
| Author:
|
Vuorinen, M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
585-608 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The rate of growth of the energy integral of a quasiregular mapping $f\:\mathcal X\rightarrow \mathcal Y$ is estimated in terms of a special isoperimetric condition on $\mathcal Y$. The estimate leads to new Phragmén-Lindelöf type theorems. (English) |
| Keyword:
|
Phragmén-Lindelöf type theorems |
| Keyword:
|
quasiregular mappings |
| Keyword:
|
isoperimetry |
| MSC:
|
30C65 |
| MSC:
|
35J60 |
| idZBL:
|
Zbl 1079.30508 |
| idMR:
|
MR1851549 |
| . |
| Date available:
|
2009-09-24T10:45:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127671 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[3] Yu. D. Burago and V. A. Zalgaller: Geometric Inequalities.Nauka, Moscow, 1980. MR 0602952 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[12] O. Martio, V. Miklyukov and M. Vuorinen: Differential forms and quasiregular mappings on Riemannian manifolds.XVIth Rolf Nevanlinna Colloquium (I. Laine and O. Martio, eds.), Walter de Gruyter &Co, 1996, pp. 151–159. MR 1427080 |
| Reference:
|
[13] O. Martio, V. Miklyukov and M. Vuorinen: Phragmén – Lindelöf’s principle for quasiregular mappings and isoperimetry.Dokl. Akad. Nauk 347 (1996), 303–305. (Russian) MR 1393057 |
| Reference:
|
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| Reference:
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[15] P. Pansu: Quasiconformal mappings and manifolds of negative curvature.Curvature and Topology of Riemannian Manifolds. Proceed. 17th Int. Taniguchi Symp., Katata, Japan, Aug. 26-31, 1985. Zbl 0592.53031, MR 0859587 |
| Reference:
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[16] E. Phragmén and E. Lindelöf: Sur une extension d’un principe classique de l’analyse et sur quelques propriétés des fonctions monogenènes dans le voisinage d’un point singulier.Acta Math. 31 (1908), 381–406. MR 1555044, 10.1007/BF02415450 |
| Reference:
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| Reference:
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[18] M. Vuorinen: Conformal Geometry and Quasiregular Mappings.Lecture Notes in Math., 1319, Springer-Verlag. Zbl 0646.30025, MR 0950174 |
| Reference:
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[19] S. T. Yau: Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold.Ann. Sci. École Norm. Sup. 8 (1975), 487–507. Zbl 0325.53039, MR 0397619, 10.24033/asens.1299 |
| . |
