for Dimitrios Betsakos

**Address**

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.

Ph.D. 1996; Advisor: Albert Baernstein.

**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] **

**[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. 105 (2022), 587-620.

[51] (with M. Boudabra, G. Markowsky) On the duration of stays of Brownian motion in domains in Euclidean space. Electronic Communications in Probability 27 (2022), Paper No. 58, 12 pp.

[52] (with A. Yu. Solynin, M. Vuorinen) Conformal capacity of hedgehogs. Conformal Geometry and Dynamics 27 (2023), 55-97.

[53] (with A. Yu. Solynin) Temperature of rods with Robin boundary conditions. J. Math. Anal. Appl. 528 (2023), Paper No. 127578, 16 pp.

[54] (with N. Karamanlis) On the monotonicity of the speeds for semigroups of holomorphic self-maps of the unit disk.

Trans. Amer.
Math. Soc. (to appear).

* *

August 2023