Gabriela Kohr

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1. Main contributions • M. Elin, S. Reich and D. Shoikhet (2000): -Parametric representation for spirallike mappings in C n and complex Banach spaces, by using the nonlinear semigroups theory 1. M. Elin, S. Reich, D. Shoikhet, Complex dynamical systems and the geometry of domains in Banach spaces, Dissertationes Math., 427(2004), 1-62. 2. S. Reich and D. Shoikhet, Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces, Imperial College Press, London, 2005. • M. Elin; I. Graham, H. Hamada, and G.K.; J.R. Muir: 1. M. Elin, Extension operators via semigroups, J. Math. Anal. Appl., 377(2011), 239-250. 2. I. Graham, H. Hamada and G.K., Extension operators and univalent subordination chains, J. Math. Anal. Appl., 386(2012), 278–289. 3. J.R. Muir, A class of Loewner chain preserving extension operators, J. Math. Anal. Appl., 337(2008), 862-979. Gabriela Kohr (UBB Cluj) Geometric and analytic aspects of Loewner chains 6 / 62
1. Main contributions • F. Bracci, M.D. Contreras, S.Diaz-Madrigal (2008): -The study of a general version of the Loewner differential equation on the unit disc and complex hyperbolic manifolds, by using the iteration and the semigroups theory 1. F. Bracci, M.D. Contreras and S.Diaz-Madrigal, Evolution families and the Loewner equation I: the unit disk, J. Reine Angew. Math., to appear. 2. F. Bracci, M.D. Contreras and S.Diaz-Madrigal, Evolution families and the Loewner equation II: complex hyperbolic manifolds, Math. Ann., 344(2009), 947-962. • M.D. Contreras, S. Diaz-Madrigal and P. Gumenyuk (2009): a general version of the notion of Loewner chains and the correspondence with the evolution families. 1. M.D. Contreras, S. Diaz-Madrigal and P. Gumenyuk, Loewner chains in the unit disk, Rev. Mat. Iberoamer., 26 (2010), 975–1012 2. M.D. Contreras, S. Diaz-Madrigal and P. Gumenyuk, Geometry behind chordal Loewner chains, Complex Analysis and Operator Theory, 4 (2010), 541–587. Gabriela Kohr (UBB Cluj) Geometric and analytic aspects of Loewner chains 7 / 62
Page 1 and 2: Geometric and analytic aspects of L
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Page 5: 1. Main contributions • I. Graham
Page 9 and 10: 2. Univalent subordination chains i
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Page 45 and 46: Remark 3. Parametric representation
Page 47 and 48: 4. Subordination chains in complex
Page 49 and 50: Theorem 4. Subordination chains in
Page 51 and 52: Theorem 4. Subordination chains in
Page 53 and 54: Remark 4. Subordination chains in c
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5. Open problems Conjecture 5. Open
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Definition 5. Open problems Let Ω
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5. Open problems References 1. P. D
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Gabriela Kohr

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