MY RESEARCH


 

My main research interests include four general areas:

1) Complex Analysis, including conformal and quasiconformal maps,
    extremal and variational problems, extremal length methods, parametric methods.

2) Free Boundary Problems of Fluid Mechanics, including Hele-Shaw flows.
    Mathematical Physics, including CFT.

3) Teichmüller Theory, including metric problems, compactification, complex structure.

4) Non-holonomic Geometry.

I have 2 monographs and about 60 published papers in these four areas. Representative recent works are:

1.

A.Vasil'ev: Moduli of families of curves for conformal and quasiconformal mappings. -
                ISBN 3-540-43846-7, Lecture Notes in Mathematics, vol. 1788,
                Springer-Verlag, Berlin- New York, 2002, 212 pp.

Ch.Pommerenke, A.Vasil'ev: Angular derivatives of bounded univalent functions and
                 extremal partitions of the unit disk.-  Pacific. J. Math.  206 (2002), no.2, 425-450.

J.M.Anderson, A.Vasil'ev: Lower Schwarz-Pick estimates and angular derivatives.-
                Ann. Acad. Sci. Fenn. 33 (2008), 101-110.

2.

B.Gustafsson, A.Vasil'ev: Conformal and potential analysis in Hele-Shaw cells. -
                  ISBN 3-7643-7703-8, Birkhäuser Verlag, 2006, 231 pp.

D.Prokhorov, A.Vasil'ev: Univalent functions and integrable systems.-
                  Comm. Math. Phys. 262 (2006), no. 2, 393-410

I.Markina, A.Vasil'ev: Explicit solutions for the Hele-Shaw corner flows with.-
                  Europ. J. Appl. Math. 15 (2004), no. 6, 771-779.

B.Gustafsson, D.Prokhorov, A.Vasil'ev: Infinite lifetime for the starlike dynamics in Hele-Shaw cells.-
                 Proc. Amer. Math. Soc. 132 (2004), no. 9, 2661-2669.

A.Vasil'ev: Energy characteristics of subordination chains.-
                  Arkiv för Matematik 45 (2007), 141-156.

3.

A.Vasil'ev, R.Hidalgo: Noded Teichmüller spaces.-
                 J. Anal. Math. 99 (2006), 89-107.

A.Vasil'ev, R.Hidalgo: Harmonic moduli of families of curves on Teichmüller spaces.-
                 Scientia. Ser. A, Math. Sci. 8 (2002), 63-73.

A.Vasil'ev: Harmonic functionals and invariant metrics in the Teichmüller spaces.-
                 Algebra and Analysis 9 (1997), no. 1, 49-71, (English  transl.:  St.-Petersburg
                 Math. J. 9 (1998), no. 1, 33-48).

4.

I.Markina, D.Prokhorov, A.Vasil'ev: Sub-Riemannian geometry of the coefficients of univalent functions.-
                 J. Funct. Analysis 245 (2007), no. 2, 475-492.

D.-Ch. Chang, I. Markina, A.Vasil'ev: Sub-Lorentzian geometry on anti-de Sitter space.-
                 J. Math. Pures Appl. 90 (2008), no.1, 82-110.

D.-Ch. Chang, I. Markina, A.Vasil'ev: Sub-Riemannian geodesics on the 3-D sphere.-
                 Compl. Anal. Oper. Theory 3 (2009), no. 2, 361-377.

 
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