Geodesic
Holomorphic Evolution: Metamorphosis of the Loewner Equations
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 1, pp. 137-165.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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Bracci, Filippo. Holomorphic Evolution: Metamorphosis of the Loewner Equations. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 1, pp. 137-165. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_1_a5/

[1] M. Abate, Iteration Theory of Holomorphic Maps on Taut Manifolds, Mediterranean Press, Rende, Cosenza, 1989. | MR | Zbl

[2] M. Abate - F. Bracci - M. D. Contreras - S. Díaz-Madrigal, The evolution of Loewner's differential equations Newsletter European Math. Soc. 78 (December 2010), 31-38. | MR | Zbl

[3] D. Aharonov - S. Reich - D. Shoikhet, Flow invariance conditions for holomorphic mappings in Banach spaces. Math. Proc. R. Ir. Acad. 99A, no. 1 (1999), 93-104. | MR | Zbl

[4] L. Arosio, Resonances in Loewner equations, Adv. Math. 227 (2011), 1413-1435. | DOI | MR | Zbl

[5] L. Arosio - F. Bracci - H. Hamada - G. Kohr, Loewner's theory on complex manifolds, J. Anal. Math., to appear.

[6] L. Arosio - F. Bracci, Infinitesimal generators and the Loewner equation on complete hyperbolic manifolds, Anal. Math. Phys., 1, 4 (2011), 337-350. | DOI | MR | Zbl

[7] L. Arosio, Basins of attraction in Loewner equations, Ann. Acad. Sci. Fenn. Math., to appear. | DOI | MR | Zbl

[8] E. Berkson - H. Porta, Semigroups of holomorphic functions and composition operators, Michigan Math. J. 25 (1978), 101-115. | MR | Zbl

[9] F. Bracci - M. D. Contreras - S. Díaz-Madrigal, Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains, J. Eur. Math. Soc. 12 (2010), 23-53. | fulltext EuDML | DOI | MR | Zbl

[10] F. Bracci - M. D. Contreras - S. Díaz-Madrigal, Evolution Families and the Loewner Equation I: the unit disc, J. Reine Angew Math. (Crelle's Journal), 672, (2012), 1-37. | DOI | MR | Zbl

[11] F. Bracci - M. D. Contreras - S. Díaz-Madrigal, Evolution Families and the Loewner Equation II: complex hyperbolic manifolds, Math. Ann. 344 (2009), 947- 962. | DOI | MR | Zbl

[12] F. Bracci - M. D. Contreras - S. Díaz-Madrigal, Semigroups versus evolution families in the Loewner theory. J. Anal. Math, 115, 1, (2011), 273-292. | DOI | MR | Zbl

[13] M. D. Contreras - S. Díaz-Madrigal - P. Gumenyuk, Loewner chains in the unit disc, Rev. Mat. Iberoamericana, 26, 3 (2010), 975-1012. | DOI | MR | Zbl

[14] M. D. Contreras - S. Díaz-Madrigal - P. Gumenyuk, Loewner Theory in annulus I: evolution families and differential equations. Trans. Amer. Math. Soc., to appear. | DOI | MR | Zbl

[15] M. D. Contreras - S. Díaz-Madrigal - P. Gumenyuk, Loewner theory in annulus II: Loewner chains. Anal. Math. Phys., 1, 4, (2011), 351-385. | DOI | MR | Zbl

[16] M. D. Contreras - S. Díaz-Madrigal - P. Gumenyuk, Local duality in Loewner equations, in preparation. | Zbl

[17] L. De Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. | DOI | MR | Zbl

[18] P. L. Duren, Univalent Functions, Springer, New York, 1983. | MR

[19] C. Earle - A. Epstein, Quasiconformal variation of slit domains. Proc. Amer. math. Soc. 129 (2001), 3363-3372. | DOI | MR | Zbl

[20] C. H. Fitzgerald - Ch. Pommerenke, The de Branges theorem on univalent functions. Trans. Amer. Math. Soc. 290, no. 2 (1985), 683-690. | DOI | MR | Zbl

[21] J. E. Fornæss - N. Sibony, Increasing sequences of complex manifolds. Math. Ann. 255 (1981), 351-360. | fulltext EuDML | DOI | MR | Zbl

[22] I. Graham - H. Hamada - G. Kohr, Parametric representation of univalent mappings in several complex variables, Canadian J. Math., 54 (2002), 324-351. | DOI | MR | Zbl

[23] I. Graham - H. Hamada - G. Kohr - M. Kohr, Asymptotically spirallike mappings in several complex variables, J. Anal. Math., 105 (2008), 267-302. | DOI | MR | Zbl

[24] I. Graham - G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker Inc., New York, 2003. | DOI | MR | Zbl

[25] I. Graham - G. Kohr - J. A. Pfaltzgraff, The general solution of the Loewner differential equation on the unit ball in $\mathbb{C}^n$, Contemporary Math. (AMS), 382 (2005), 191-203. | DOI | MR | Zbl

[26] H. Hamada - G. Kohr - J. R. Muir, Extension of $L^d$-Loewner chains to higher dimensions. Preprint, 2011. | DOI | MR

[27] W. Kager - B. Nienhuis - L. P. Kadanoff, Exact solutions for Loewner evolutions. J. Statist. Phys. 115, 3-4 (2004), 805-822. | DOI | MR | Zbl

[28] S. Kobayashi, Hyperbolic complex spaces. Springer-Verlag Berlin Heidelberg, 1998 | DOI | MR | Zbl

[29] P. P. Kufarev, On one-parameter families of analytic functions, (in Russian) Mat. Sb. 13 (1943), 87-118. | fulltext EuDML | MR

[30] P. P. Kufarev, On integrals of a very simple differential equation with movable polar singularity in the right hand side (in Russian) Tomsk. Gos. Univ. Uchen. Zap. no. 1 (1946), 35-48. | MR

[31] P. P. Kufarev, A remark on the integrals of the Loewner eqaution, Dokl. Akad. Nauk. SSSR, 57 (1947), 655-656 (in Russian). | MR

[32] P. P. Kufarev - V. V. Sobolev - L. V. Sporysheva, A certain method of investigation of extremal problems for functions that are univalent in the half-plane, Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 200 (1968), 142-164. | MR

[33] G. F. Lawler, Conformally invariant processes in the plane, Mathematical surveyes and monograph, vol. 114, Amer. Math. Soc. (2005). | MR | Zbl

[34] G. F. Lawler - O. Schramm - W. Werner, Values of Brownian intersection exponents. I. Half-plane exponents, Acta Math. 187 (2001), 237-273. | DOI | MR | Zbl

[35] G. F. Lawler - O. Schramm - W. Werner, Values of Brownian intersection exponents. II. Plane exponents, Acta Math. 187 (2001), 275-308. | DOI | MR | Zbl

[36] K. Loewner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, Math. Ann. 89 (1923), 103-121. | fulltext EuDML | DOI | MR

[37] J. R. Lind, A sharp condition for the Loewner equation to generate slits, Ann. Acad. Sci. Fenn. Math. 30, 1 (2005), 143-158. | fulltext EuDML | MR | Zbl

[38] D. E. Marshall - S. Rohde, The Loewner differential equation and slit mappings, J. Amer. Math. Soc. 18 (2005), 763-778. | DOI | MR | Zbl

[39] J. A. Pfaltzgraff, Subordination chains and univalence of holomorphic mappings in $\mathbb{C}^n$, Math. Ann., 210 (1974), 55-68. | fulltext EuDML | DOI | MR | Zbl

[40] J. A. Pfaltzgraff, Subordination chains and quasiconformal extension of holomorphic maps in $\mathbb{C}^n$, Ann. Acad. Scie. Fenn. Ser. A I Math., 1 (1975), 13-25. | MR | Zbl

[41] D. Prokhorov - A. Vasil'Ev, Singular and tangent slit solutions to the Löwner equation, in Analysis and Mathematical Physics, Trends in Mathematics (Birkhuser Verlag, 2009), 455-463. | DOI | MR

[42] Ch. Pommerenke, Über dis subordination analytischer funktionen, J. Reine Angew Math. 218 (1965), 159-173. | fulltext EuDML | DOI | MR | Zbl

[43] Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975. | MR

[44] T. Poreda, On generalized differential equations in Banach spaces, Dissertationes Mathematicae, 310 (1991), 1-50. | fulltext EuDML | MR | Zbl

[45] S. Reich - D. Shoikhet, Metric domains, holomorphic mappings and nonlinear semigroups, Abstr. Appl. Anal. 3, no. 1-2 (1998), 203-228. | fulltext EuDML | DOI | MR | Zbl

[46] S. Reich - D. Shoikhet, Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces, Imperial College Press, London, 2005. | DOI | MR

[47] O. Schramm, Scaling limits of loop-erased random walks and uniform spanning trees, Israel J. Math. 118 (2000), 221-288. | DOI | MR | Zbl

[48] M. Voda, Solution of a Loewner chain equation in several variables, J. Math. Anal. Appl. 375, no. 1 (2011), 58-74. | DOI | MR | Zbl