Farit Avkhadiev

Doctor of Phys. and Math. Sciences, Professor, Senior research fellow, 
Head of the Department

Degrees

04/1991 - doctor (Physics and Mathematics)

specialty 01.01.01 -  Real, Complex and Functional Analysis

thesis title “Geometric properties of conformal and locally quasiconformal mappings with given boundary behavior”

Research Interests

• Geometric function theory
• Isoperimetric problems and boundary-value problems of  Mathematical Physics
• Extremal problems of Complex Analysis
• Integral inequalities, in particular, Hardy-Rellich type inequalities in domains of the Euclidean space.

^{Modern Problems of Mathematics}

^{Geometric Function Theory}

Taught Disciplines

• Numerical Methods
• Geometric Function Theory
• Extremal Problems of Function Theory
• Modern Problems of Mathematics

Main publications (in English)

• Avkhadiev,F G, and Aksent'ev, LA.  The main results on sufficient conditions for an analytic function to be schlicht. Russian Math. Surveys, 1975, v.. 30, № 4, pp 3-63.
• Avkhadiev,F G, and  Maklakov, DV. A Theory of Pressure envelopes for Hydrofoils. Ship technology research schiffstechnik. 1995, v. 42, No.2,  pp 81-102.
• Avkhadiev,F G. Solution of the generalized Saint Venant problem. Sbornik Mathematics, 1998, v. 189, No. 12, pp 1739-1748.
• Avkhadiev,F G. Hardy-type inequalities on planar and spatial open sets. Proceedings of the Steklov institute of Mathematics, 2006, v. 255, No. 1, pp 2-12.
• Avkhadiev,F G, Pommerenke, Ch, and  Wirths, K.-J. Sharp inequalities for the coefficients of concave schlicht functions. Comm. Math. Helvetici, 2006, v.81, pp 801-807.
• Avkhadiev,F G, and Wirths, K-J. Unified  Poincar\'{e} and Hardy inequalities with sharp constants for convex domains. Z. Angew. Math. Mech. (ZAMM), 2007, v. 87, No.8-9, pp 632-642.
• Avkhadiev,F G, and Wirths, K-J. Schwarz-Pick Type Inequalities,  Basel-Boston-Berlin,  Birkh\"auser Verlag,  2009, 156 рр.
• Avkhadiev,F G. A geometric des­cription of domains whose Hardy constant is equal to ¼. Izvestiya: Mathematics, 2014, v.78, No. 5, pp 855-876.
• Avkhadiev,F G. Integral inequalities in domains of hyperbolic type and their applications. Sbornik Mathematics., 2015, v. 206, No. 12, pp 1657-1681.
• Avkhadiev,F G. Hardy-Rellich inequalities in domains of the Euclidean space.   J. Math. Anal. Appl., 2016, v. 442, pp 469-484.

^{Numerical Methods}