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References
Bishop C. J., Brownian motion in Denjoy domains, Ann. Prob. (to appear).
Bishop C. J., A characterization of Poissonian domains, Arkiv Mat. (to appear).
Bishop C. J., Jones P. W., Harmonic measure and arclength, Ann. Math. 132 (1990), 511–547.
Bishop C. J., Jones P. W., Harmonic measure, L2 estimates and the Swarzian derivative, preprint, 1990.
Bourgain J., On the Hausdorff dimension of harmonic measure in higher dimensions, Inv. Math 87 (1987), 477–483.
Jones P. W. and Wolff T. H., Hausdorff dimension of harmonic measures in the plane, Acta. Math. 161 (1988), 131–144.
Makarov N. G., On distortion of boundary set under conformal mappings, Proc. London Math. Soc. 51 (1985), 369–384.
Pommerenke Ch., On conformal mapping and linear measure, J. Analyse Math. 46 (1986), 231–238.
Wolff T. H., Counterexamples with harmonic gradients, preprint, 1987.
References
Korenblum B., AMS Abstracts, 855-30-04 (1990).
Korenblum B., A maximum principle for the Bergman space, Publications Matemátiques (Barcelona) (to appear).
Korenblum B., Transformations of zero sets by contractive operators in the Bergman space, Bull. Sc. Math. 2e série 114 (1990), 385–394.
Korenblum B., Richards K., Majorization and domination in the Bergman space, preprint.
Korenblum B., O’Neil R., Richards K., Zhu K., Totally monotone functions with applications to the Bergman space, preprint.
References
Luecking D., Zhu K., Composition operators belonging to Schatten classes, Amer. J. Math (to appear).
MacCluer B., Shapiro J., Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canadian J. Math. 38 (1986), 878–906.
Sarason D., Angular derivatives via Hilbert space, Complex Variables 10 (1988), 1–10.
Shapiro J., The essential norm of a composition operator, Ann. Math. 12 (1987), 375–404.
References
Goodman A. W., Univalent functions, Vols. I and II, Polygonal Publishing House, Washington, New Jersey U.S.A., 1983.
Goodman A. W., Topics in mathematical analysis, World Scientific Publishing Co., Singapore, 1989.
Goodman A. W., Convex functions of bounded type, Proc. Amer. Math Soc. 92 (1984), 541–546.
Goodman A. W., More on convex functions of bounded type, Proc. Amer. Math Soc. 97 (1986). 303–306.
Goodman A. W., On uniformly starlike functions, Jour. of Math. Analysis and Appl. 155 (1991), 364–370.
Goodman A. W., On uniformly convex functions, Ann. Polo. Math. (to appear).
Ma Wancang, Mejia Diego, Minda David, Distortion theorems for euclidean k-convex functions, Complex Var. Theor. and Appl. (to appear).
Ma Wancang, Mejia Diego, Minda David, Distortion theorems for hyperbolically and spherically k-convex functions, Proc. Inter. Conf. New Trends in Geom. Func. Th. and Appl. (to appear).
Mejia Diego, Minda David, Hyperbolic geometry in k-convex regions, Pac. Jour. of Math. 141 (1990), 333–354.
Mejia Diego, Minda David, Hyperbolic geometry in spherically k-convex regions, Comp. Methods and Func. Th. Proc., Lecture notes in Math, vol. 1435, Springer, 1990.
Mejia Diego, Minda David, Hyperbolic geometry in hyperbolically k-convex regions, submitted.
Wirths K. J., Coefficient bounds for convex functions of bounded type, Proc. Amer. Math. Soc. 103 (1988), 525–530.
References
Krzyż J. G., Quasicircles and harmonic measure, Ann. Acad. Sci. Fenn. Ser. A I Math. 12 (1987), 19–24.
Krzyż J. G., Harmonic analysis and boundary correspondence under quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), 225–242.
References
de Branges L., A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137–152.
Bshouty D., Hengartner W., Criteria for the extremality of the Koebe mapping, Proc. Amer. Math. Soc. 111 (1991), no. 2, 403–411.
Duren P. L., Univalent Functions, Springer Verlag, Heidelberg-New York, 1983.
Golusin G. M., Geometric Theory of Functions of a Complex Variable, “Nauka”, Moscow, 1966 (Russian); English transl. Amer. Math. Soc., 1969.
Grinshpan A. Z., On the Taylor coefficients of certain classes of univalent functions, Metric Questions in the Theory of Functions, “Naukova Dumka”, Kiev, 1980, pp. 28–32. (Russian).
Grinshpan A. Z., On coefficients of powers of univalent functions, Sibirsk. Mat. Zh. 22 (1981), no. 4, 88–93 (Russian); English transl. in Siberian Math. J. 22 (1981), 551–555.
Grinshpan A. Z., On the power stability for the Bieberbach inequality, Zap. Nauchn. Sem. LOMI 125 (1983), 58–64. (Russian).
Grinshpan A. Z., Method of exponentiation for univalent functions, Theory of Functions and Applications, Proc. Conf. Saratov, 1988, Part 2, Izdat. Sar. Univ., Saratov, 1990, pp. 72–74. (Russian)
Grinshpan A. Z., Univalent functions with prescribed logarithmic restrictions, Annals Polonici Mathematici (to appear).
Milin I. M., Grinshpan A. Z., Logarithmic coefficients means of univalent functions, Complex Variables: Theory and Appl. 7 (1986), no. 1-3, 139–147.
Milin I. M., Univalent Functions and Orthonormal Systems, “Nauka”, Moscow, 1971 (Russian); English transl. Amer. Math. Soc., Providence, R.I., 1977.
References
De Branges L., Unitary linear systems whose transfer functions are Riemann mapping functions, Integral Equations and Operator Theory 19 (1986), 105–124.
De Branges L., Underlying concepts in the proof of the Bieberbach conjecture, Proceedings of the International Congress of Mathematicians 1986, Berkeley, California, 1986, pp. 25–42.
De Branges L., Square Summable Power Series, Springer-Verlag, in preparation.
Li Kin Y., Rovnyak James, On the coefficients of Riemann mappings of the unit disk into itself, 1991, preprint.
Rovnyak J., Coefficient estimates for Riemann mapping functions, J. Anal. Math. 52 (1989), 53–93.
References
Tamrazov P. M., Smoothness and Polynomial Approximations, Naukova Dumka, Kiev, 1975. (Russian)
Näkki R., Palka B., Extremal length and Hölder continuity of conformal mappings, Comment. Math. Helvetici 61 (1986), 389–414.
Belyî V. I., On moduli of continuity of exterior and interior conformal mappings of the unit disk, Ukranian Math. J. 41, (1989), no. 4, 469–475. (Russian).
References
Baerstein A., An extremal problem for certain subharmonic functions in the plane, Rev. Mat. Iberoamericana 4 (1988), 199–219.
Cassels J. W. S., An introduction to the Geometry of numbers (2nd ed.), Springer, Berlin, 1972.
Fryntov A. E., An extremal problem of potential theory, Dokl. Akad. Nauk USSR 300 (1988), no. 4 (Russian); English transl. in Soviet Math.—Doklady 37 (1988), 754–755.
Hayman W. K., Subharmonic functions, vol. 2, Academic Press, London, 1989.
Hille E., Analytic Function Theory, vol. 2, Ginn, Boston, 1962.
Minda C. D., Bloch constants, J. Analyse Math. 41 (1982), 54–84.
Montgomery H., Minimal theta functions, Glasdow Math. J. 30 (1988), 75–83.
Osgood B., Phillips R., Sarnak P., Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), 148–211.
Quine J. R., Heydari S. H., Song R. Y., Zeta regularized products, Trans. Amer. Math. Soc. (to appear).
Rogers C. A., Packing and Covering, Cambridge U. P., Cambridge, 1964.
Weitsman A., Symmetrization and the Poincaré metric, Annals of Math. 124 (1986), 159–169.
References
Abu-Muhanna Y., Lyzzaik A., The boundary behaviour of harmonic univalent maps, Pacific J. Math. 141 (1990), 1–20.
Clunie J., Sheil-Small T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A.I 9 (1984), 3–25.
Hengartner W., Schober G., Harmonic mappings with given dilatation, J. London Math. Soc. 33 (1986), 473–483.
Hengartner W., Schober G., Curvature estimates for some minimal surfaces, Complex Analysis: Articles dedicated to Albert Pfluger on the occasion of his 80th birthday (Hersch J., Huber A., eds.), Birkhäuser Verlag, Basel, 1988, pp. 87–100.
Lewy H., On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc. 42 (1936), 689–692.
Nitsche J. C. C., On the module of double-connected regions under harmonic mappings, Amer. Math. Monthly 69 (1962), 781–782.
Schober G., Planar harmonic mappings, Computational Methods and Function Theory, Lecture Notes in Math., Springer-Verlag, Berlin-Heidelberg, 1990, pp. 171–176.
Sheil-Small, T., Constants for planar harmonic mappings, J. London Math. Soc. 42 (1990), 237–248.
References
Alan F. Beardon and Kenneth Stephenson, The Schwarz-Pick lemma for circle packings, Ill. J. Math. 141 (1991), 577–606.
Alan F. Beardon and Kenneth Stephenson, The uniformization theorem for circle packings, Indiana Univ. Math. J., 39 (1990), 1383–1425.
Koebe P., Kontaktprobleme der Konformen Abbildung, Ber. Sächs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 88 (1936), 141–164.
Burt Rodin and Dennis Sullivan, The convergence of circle packings to the Riemann mapping, J. Differential Geometry 26 (1987), 349–360.
Kenneth Stephenson, Circle packings in the approximation of conformal mappings, Bulletin, Amer. Math. Soc. (Research Announcements) 23 (1990), no. 2, 407–415.
Kenneth Stephenson, Thurston’s conjecture on circle packings in the nonhexagonal case, preprint.
William Thurston, The Geometry and Topology of 3-Manifolds, preprint, Princeton University Notes.
References
Milin I. M., On a property of logarithmic coefficients on univalent functions, Metric questions of the function theory, Naukova Dumka, Kiev, 1980, pp. 86–90. (Russian)
Lebedev N. A., An application of the area principle to problems on non overlapping domains, Trudy Mat. Inst. Akad. Nauk SSSR 60 (1961), 211–231. (Russian)
Milin I. M., On a conjecture on a logarithmic coefficients of univalent functions, Zapiski nauchn. semin. LOMI 125 (1983), 135–143 (Russian); English transl. in J. Soviet Math. 26 (1984), no. 6.
References
Astala K., Fernández J. L., Rohde S. (1991) (to appear).
Astala K., Zinsmeister M., Teichmüller spaces and BMOA, Mittag-Leffler Report 20 (1989–90).
Bishop C. J., Jones P. W. Harmonic measure, L2-estimates and the Schwarzian derivative, preprint (1990).
Fernández J. L., Heinonen J., Martio O., Quasilines and conformal mappings, J. Analyse Math. 52 (1989), 117–132.
Garnett J. B., Gehring F. W., Jones P. W., Conformally invariant length sums, Indiana Univ. Math. J. 32 (1983), 809–829.
Haiman W. K., Wu J.-M., Level sets of univalent functions, Comment. Math. Helv. 56 (1981), 366–403.
Jones P. W., Marshall D. E., Critical points of Green’s function, harmonic measure and the corona problem, Ark. Math. 23 (1985), 281–314.
Øyma K., Harmonic measure and conformal length, Proc. Amer. Math. Soc. (to appear).
Väisälä J, Bounded turning and quasiconformal maps, Monatsch. Math. (to appear).
References
Brown J. E., Geometric properties of a class of support points of univalent functions, Trans. Amer. Math. Soc. 256 (1979), 371–382.
Brown J. E., Univalent functions maximizing Re{a 3+λa 2}, Illinois J. Math. 25 (1981), 446–454.
Duren P. L., Arcs omitted by support points of univalent functions, Comment. Math. Helv. 56 (1981), 352–365.
Duren P. L., Univalent Functions, Springer-Verlag, New York, 1983.
Hamilton D. H., On Littlewood’s conjecture for univalent functions, Proc. Amer. Math. Soc. 86 (1982) 32–36.
Pearce K., New support points of S and extreme points of HS, Proc. Amer. Math. Soc. 81 (1981), 425–428.
References
Hayman W. K., Wu J.-M. G., Level sets of univalent functions, Comm. Math. Helv. 56 (1981), 366–403.
Garnett J. B., Gehring F. W., Jones P. W. Conformally invariant length sums, Indiana Univ. Math. J. 32 (1983), 809–829.
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Duren, P. (1994). Geometric function theory. In: Havin, V.P., Nikolski, N.K. (eds) Linear and Complex Analysis Problem Book 3. Lecture Notes in Mathematics, vol 1574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101068
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