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Conformal radius: At the interface of traditions

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dc.contributor.author Kazantsev A.
dc.date.accessioned 2018-09-19T22:11:16Z
dc.date.available 2018-09-19T22:11:16Z
dc.date.issued 2017
dc.identifier.issn 1995-0802
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/144834
dc.description.abstract © 2017, Pleiades Publishing, Ltd.H. Behnke’s and E. Peschl’s definition of plänarkonvexitat leads to the Epstein-type inequalities when applies to the Hartogs domains in C2. One-parameter series of such inequalities reveals the following rigidity phenomenon: the set of the parameters with contensive inequalities is exactly the segment which center corresponds to the well-known Nehari ball. The latter plays the crucial role in the forming the Gakhov class of all holomorphic and locally univalent functions in the unit disk with no more than one-pointed null-sets of the gradients of their conformal radii. The sufficient condition for the piercing of the Nehari sphere out of the Gakhov class is found. We deduce such a condition along the lines of the subordination approach to the proof of Haegi’s theorem about the inclusion of any convex holomorphic function into the Gakhov class.
dc.relation.ispartofseries Lobachevskii Journal of Mathematics
dc.subject Conformal radius
dc.subject Epstein inequality
dc.subject Gakhov class
dc.subject Gakhov equation
dc.subject Hartogs domain
dc.subject hyperbolic derivative
dc.subject linear convexity
dc.subject linear-invariant family
dc.title Conformal radius: At the interface of traditions
dc.type Article
dc.relation.ispartofseries-issue 3
dc.relation.ispartofseries-volume 38
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 469
dc.source.id SCOPUS19950802-2017-38-3-SID85019710504


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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