# Curriculum Vitae for Dimitrios Betsakos

Department of Mathematics,
Aristotle University of Thessaloniki,
54124 Thessaloniki, Greece.

Telephone number: 30 2310 997935
E-mail: betsakos@math.auth.gr
Web site: http://users.auth.gr/~betsakos

Education
1. Department of Mathematics, Aristotle University of Thessaloniki 1986-1990. B.Sc. 1990.
2. Department of Mathematics, Washington University, St.Louis, 1991-1996. M.Sc. 1994.

Research Interests
Complex analysis, potential theory, geometric function theory, conformal mapping, harmonic measure, capacity, extremal length, hyperbolic metric, Brownian motion, probabilistic potential theory, semigroups of holomorphic functions, composition operators.

Employment
1. 1998-1999: Postdoctoral Fellow, Department of Mathematics, University of Helsinki.
2. 1999-2000: Visiting assistant professor, School of Engineering, Aristotle University of Thessaloniki.
3. 2000-2002: Visiting assistant professor, Department of Applied Mathematics, University of Crete.
4. 2002-2008: Assistant professor, Department Mathematics, Aristotle University of Thessaloniki.
5. 2008-2014: Associate professor, Department Mathematics, Aristotle University of Thessaloniki.

6. 2014-       : Professor, Department Mathematics, Aristotle University of Thessaloniki.

Publications
[1] On certain harmonic measures on the unit disk. Colloquium Math.73 (1997), 221-228.

[2] Harmonic measure on simply connected domains of fixed inradius. Ark. Mat. 36 (1998), 275-306.

[3] Polarization, conformal invariants and Brownian motion. Ann. Acad. Sci. Fenn. Ser. A I Math. 23 (1998), 59-82.

[4] On bounded univalent functions that omit two given values. Colloquium Math. 80 (1999), 253-258.

[5] An extension of the Beurling-Nevanlinna projection theorem. Computational Methods in Function Theory (CMFT'97). N.Papamichael, St.Ruscheweyh and E.Saff (Eds.), pp.87-90. World Scientific, 1999.

[6] On conformal capacity and Teichm\"uller's modulus problem in space.
Journal d'Analyse Mathematique 79 (1999), 201-214.
[7] (with A.Yu.Solynin) Extensions of Beuring's shove theorem for harmonic measure. Complex Variables 42 (2000), 57-65.
[8] (with M.Vuorinen) Estimates for conformal capacity. Constructive Approximation 16 (2000), 589-602.

[9] On the equilibrium measure and the capacity of certain condensers.
Illinois J. Math. 44 (2000), 681-689.
[10] Geometric theorems and problems for harmonic measure. Rocky Mountain J. of Math. 31 (2001), 773-795.
[11] Extremal problems for extremal distance and harmonic measure. Complex Variables 45 (2001), 201-212.

[12] Hitting probabilities of conditional Brownian motion and polarization. Bulletin Australian. Math. Soc. 66 (2002), 233-244.
[13] (with A.Yu Solynin) On the distribution of harmonic measure on simply connected planar domains. Journal Australian Math. Soc. 75 (2003), 145-151.

[14] Two point projection estimates for harmonic measure. Bulletin London Math. Soc. 35 (2003), 473-478.

[15] On separating conformal annuli and Mori's ring domain in $R^n$. Israel J. of Math. 133 (2003), 1-8.

[16] Symmetrization, symmetric stable processes, and Riesz capacities. Trans. Amer. Math. Soc. 356 (2004), 735-755. Addendum 356 (2004), 3821.

[17] Polarization, continuous Markov processes and second order elliptic equations. Indiana Univ. Math. J. 53 (2004), 331-346.

[18] (with K.Samuelsson and M.Vuorinen) The computation of capacity of planar condensers. Publ. Inst. Math. 75 (89) (2004), 233-252.

[19] Elliptic, hyperbolic, and condenser capacity; geometric estimates for elliptic capacity. Journal d'Analyse Mathematique 96 (2005), 37--55.
[20] (with S.Grigoriadou) On the determination of a measure by the orbits generated by its logarithmic potential. Proc. Amer. Math. Soc. 134 (2006), 541--548.
[21] Estimation of the hyperbolic metric by using the punctured plane. Math. Z. 259 (2008), 187--196.

[22] Some properties of $\alpha$-harmonic measure. Colloq. Math. 111 (2008), 297-314.

[23] Equality cases in the symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels. Ann. Acad. Sci. Fenn. Ser. A I Math. (2008), 413--427.

[24] Symmetrization and harmonic measure.
Illinois J. Math. 52 (2008), 919-949.
[25] An extremal problem for the hyperbolic metric on Denjoy domains. Comp. Methods Function Theory  10 (2010), 49-59.
[26] Geometric versions of Schwarz's lemma for quasiregular mappings. Proc. Amer. Math. Soc. 139 (2011), 1397-1407.
[27] Multi-point variations of Schwarz lemma with diameter and width conditions. Proc. Amer. Math. Soc. 139 (2011), 4041-4052.

[28] (with S.Pouliasis) Equality cases for condenser capacity inequalities under symmetrization. Annales Univ. Mariae Curie-Skłodowska 66 (2012), 1-24.

[29] (with S.Pouliasis) Versions of Schwarz's lemma for condenser capacity and inner radius. Canadian Math. Bul. 56 (2013), 241-250.

[30] Holomorphic functions with image of given logarithmic or elliptic capacity. J. Australian Math. Soc.  94  (2013), 145-157.

[31] Hyperbolic geometric versions of Schwarz's lemma. Conformal Geometry and Dynamics 17 (2013), 119-132.

[32] Estimates for convex integral means of harmonic functions. Proc. Edinb. Math. Soc. 57 (2014),  619–630.

[33] On the images of horodisks under holomorphic self-maps of the unit disk. Archiv der Math. (Basel) 102 (2014), 91–99.
[34] Lindelof's principle and estimates for holomorphic functions involving area, diameter, or integral means. Comp. Methods Function Theory  14 (2014), 85-105.

[35] On the existence of strips inside domains convex in one direction. Journal d'Analyse Mathematique 134 (2018), 107-126.

[36] On the asymptotic behavior of the trajectories of semigroups of holomorphic functions.J. Geometric Analysis 26 (2016), 557-569.

[37] On the rate of convergence of parabolic semigroups of holomorphic functions.Analysis and Math. Physics 5 (2015), 207-216.

[38] On the rate of convergence of hyperbolic semigroups of holomorphic functions. Bulletin London Math. Soc. 47 (2015), 493-500.

[39] Geometric description of the classification of holomorphic semigroups. Proc. Amer. Math. Soc. 144 (2016), 1595-1604.

[40] On the eigenvalues of the infinitesimal generator of a  semigroup of composition operators. J. Funct. Anal. 273 (2017), 2249-2274.

[41] On the eigenvalues of the infinitesimal generator of a  semigroup of composition operators on Bergman spaces. Bulletin Hellenic Math. Soc. 61 (2017), 41-54.

[42] (with S.Pouliasis)  Isometries for the modulus metric are quasiconformal mappings. Trans. Amer.  Math. Soc.  372  (2019), 2735-2752.

[43] Angular derivatives and compactness of composition operators on Hardy spaces. J. Operator Theory 82  (2019),  189-196.

[44] (with G.Kelgiannis, M.Kourou, S.Pouliasis)  On the asymptotic behavior of condenser capacity under Blaschke products and universal covering maps. Proc. Amer. Math. Soc. 147 (2019), 2963-2973.

[45] (with G.Kelgiannis, M.Kourou, S.Pouliasis)  Semigroups of holomorphic functions and condenser capacity.   Analysis and Math. Physics  10 (2020), 18 pp.

[46] (with M. D. Contreras, S. Diaz-Madrigal)  On the rate of convergence of semigroups of holomorphic functions at the Denjoy-Wolff point.  Revista Mathematica Iberoamericana 36 (2020), 1659-1686.

[47] (with M. Boudabra, G. Markowsky)  On the probability of fast exits and long stays of planar Brownian motion in simply connected domains. J. Math. Anal. Appl. 493 (2021),  10 pp.

[48] (with C. Karafyllia, N. Karamanlis)  Hyperbolic metric and membership of conformal maps in the Bergman space. Canadian Math. Bul. 64 (2021), 174-181.

[49] (with A.Yu. Solynin) Heating long pipes, Analysis and Math. Physics 11 (2021), 35 pp.

[50] (with N. Karamanlis)  Conformal invariants and the angular derivative problem.  J. London Math. Soc. (to appear).

March 2021