Geodesic
Geometric versions of Schwarz lemma and symmetrization
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 63-76

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Connection between the geometric versions of Schwarz lemma and the known symmetrization principles for some classes of analytic functions in a disk and a circular ring are discussed. In particular, simple proofs based on classical approaches are presented for some resent results of other authors. Bibl. 22 titles. 
@article{ZNSL_2010_383_a3,
     author = {V. N. Dubinin},
     title = {Geometric versions of {Schwarz} lemma and symmetrization},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {63--76},
     publisher = {mathdoc},
     volume = {383},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a3/}
}
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V. N. Dubinin. Geometric versions of Schwarz lemma and symmetrization. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 63-76. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a3/