Geometric Function Theory in One and Higher Dimensions

By Ian D. Graham, G. Kohr. 2003

555 citations recorded by the source corpus.

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In Geometry and Topology

Citations in the corpus

An abstract approach to Loewner chains (2010, methodology): “In the case f(0) = 0, the inequality in the third statement becomes the well known analytic characterization of star-likeness for locally univalent mappings on B (see [12], [16], [32] and the references therein).”
Asymptotically spirallike mappings in several complex variables (2008, methodology): “If n = 1, S(U) = S (see [31]), but S(B) $ S(B) for n ≥ 2 (see [9] and [14]).”
Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings (2012, background): “alent function f. For more properties and results related to the pre-Schwarzian and Schwarzian derivatives of locally univalent analytic mappings, we refer the reader to the monographs [23], [12], or [15]. PRE-SCHWARZIAN AND SCHWARZIAN DERIVATIVES OF HARMONIC MAPPINGS 3 A deﬁnition of the Schwarzian”
Evolution families and the Loewner equation II: complex hyperbolic manifolds (2008, methodology): “[8] I. Graham, G. Kohr, M. Kohr, Loewner chains and parametric representation in several complex variables.”
A class of Loewner chain preserving extension operators (2008, background): “A discussion of these topics is provided in Chapter 8 of the monograph [4] of Graham and Kohr.”
Variation of Loewner Chains, Extreme and Support Points in the Class $$S^0$$S0 in Higher Dimensions (2014, background): “(ii) It is known that S0 is compact in the topology of uniform convergence on compacta, and that S0 = S for n ≥ 2 (see [19]; see also [12] and [18]).”
A Modification of the Roper-Suffridge Extension Operator (2005, methodology): “A good treatment of further applications of the Roper–Suffridge extension operator can be found in the recent book by Graham and Kohr [3].”
Bohr radius for certain classes of starlike and convex univalent functions (2020, background): “For more properties of starlike and convex functions, we refer the reader to [18, 21, 46].”
The evolution of Loewner's differential equations (2010, background): “Anyway, many natural cases, such as spiral-like maps, can be treated efficiently, and many applications and estimates can be obtained (see [25]).”