Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains
Connection of an exterior inverse boundary value problem with the critical points of some surface is one of the central themes in the theory of exterior inverse boundary value problems for analytic functions. In the simply connected case, such a surface is defined by the inner mapping radius; in the...
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Kazan Federal University
2017-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | http://kpfu.ru/portal/docs/F1966836537/159_1_phys_mat_4.pdf |
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| author | A.V. Kazantsev |
| author_facet | A.V. Kazantsev |
| author_sort | A.V. Kazantsev |
| collection | DOAJ |
| description | Connection of an exterior inverse boundary value problem with the critical points of some surface is one of the central themes in the theory of exterior inverse boundary value problems for analytic functions. In the simply connected case, such a surface is defined by the inner mapping radius; in the multiply connected one, by the function Ω(w) such that M(w) = (2π)–1ln Ω(w) is Mityuk's version of a generalized reduced module. In the present paper, the relation between the curvature of the surface Ω = Ω(w) with the Schwarzian derivatives of the mapping functions and with the Bergman kernel functions k0(w,ω) and l0(w,ω) is established for an arbitrary multiply connected domain. When passing to two-connected domains, due to the choice of the ring as a canonical domain, we construct the conditions for the critical points of Mityuk's radius to concentrate on the golden section circle of the ring. Finally, we show that the minimal collection of the critical points of the Mityuk radius in the two-connected case, consisting of one maximum and one saddle, is attained for the linear-fractional solution of the exterior inverse boundary value problem. |
| format | Article |
| id | doaj-art-4a17b3e1e7e3445d87b40646b0eaa91f |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2017-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-4a17b3e1e7e3445d87b40646b0eaa91f2025-01-02T20:44:23ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982017-03-0115913346Sectio Aurea Conditions for Mityuk's Radius of Two-Connected DomainsA.V. Kazantsev0Kazan Federal University, Kazan, 420008 RussiaConnection of an exterior inverse boundary value problem with the critical points of some surface is one of the central themes in the theory of exterior inverse boundary value problems for analytic functions. In the simply connected case, such a surface is defined by the inner mapping radius; in the multiply connected one, by the function Ω(w) such that M(w) = (2π)–1ln Ω(w) is Mityuk's version of a generalized reduced module. In the present paper, the relation between the curvature of the surface Ω = Ω(w) with the Schwarzian derivatives of the mapping functions and with the Bergman kernel functions k0(w,ω) and l0(w,ω) is established for an arbitrary multiply connected domain. When passing to two-connected domains, due to the choice of the ring as a canonical domain, we construct the conditions for the critical points of Mityuk's radius to concentrate on the golden section circle of the ring. Finally, we show that the minimal collection of the critical points of the Mityuk radius in the two-connected case, consisting of one maximum and one saddle, is attained for the linear-fractional solution of the exterior inverse boundary value problem.http://kpfu.ru/portal/docs/F1966836537/159_1_phys_mat_4.pdfexterior inverse boundary value problemmultiply connected domainGakhov equationMityuk's radiusinner mapping (conformal) radiushyperbolic derivative |
| spellingShingle | A.V. Kazantsev Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains Учёные записки Казанского университета: Серия Физико-математические науки exterior inverse boundary value problem multiply connected domain Gakhov equation Mityuk's radius inner mapping (conformal) radius hyperbolic derivative |
| title | Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains |
| title_full | Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains |
| title_fullStr | Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains |
| title_full_unstemmed | Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains |
| title_short | Sectio Aurea Conditions for Mityuk's Radius of Two-Connected Domains |
| title_sort | sectio aurea conditions for mityuk s radius of two connected domains |
| topic | exterior inverse boundary value problem multiply connected domain Gakhov equation Mityuk's radius inner mapping (conformal) radius hyperbolic derivative |
| url | http://kpfu.ru/portal/docs/F1966836537/159_1_phys_mat_4.pdf |
| work_keys_str_mv | AT avkazantsev sectioaureaconditionsformityuksradiusoftwoconnecteddomains |