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New applications of the circular symmetrization to the multivalent functions

Colloquium in Mathematics and Computer Science,
New applications of the circular symmetrization to the multivalent functions

Prof. Vladimir Dubinin, Far Eastern Federal University, Russia
May 21, at 11:00 Science Building 8, Room 424

Earlier we proposed a new version of the circular symmetrization of the condensers on the Riemann surfaces [1]. This transformation of condensers allows to obtain new results taking into account the ramification points of the surfaces (for more details, see [2]). In the present talk, we discuss the applications of the symmetrization to p-valent functions, circumferentially mean p-valent functions and complex polynomials [3]-[6].
 
References:
  1. V.N.Dubinin, A new version of circular symmetrization with applications to p-valent functions, Sbornik: Mathematics, 203:7 (2012), 996–1011.
  2. V. N. Dubinin, Circular symmetrization of condensers on the Riemann surfaces, Mat. Sb., 206:1 (2015), 69–96.
  3. V.N.Dubinin, Symmetrization of condensers and inequalities for functions multivalent in a disk, Math. Notes. 94:6 (2013) , 876–884.
  4. V.N.Dubinin, On the Jenkins covering circle theorem for holomorphic functions in a disk, Journal of Mathematical Sciences (New York), 200:5 (2014), 551–558.
  5. V.N.Dubinin, On one extremal problem for complex polynomials with constraints on critical values, Siberian Math. Journal, 55:1(2014), 63–71.
  6. V.N.Dubinin, Inequalities for moduli of the circumferentially mean p-valent functions, Zap. Nauchn. Sem. POMI, 429 (2014), 44–54.
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