ON HARMONIC FUNCTIONS AND THE SCHWARZ LEMMA
By David Kalaj, Matti Vuorinen. 2010
102 citations recorded by the source corpus.
We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a1f80e6894eb02b626d31d2cf33595122aeaed7a
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Bohr radius for locally univalent harmonic mappings (2017, unknown): “= 3 √ 3 4 r − a 1−ar 2 − a2 +4a(1− a2)r ! . Now we suppose that r is a function of a. We want to find the minimal r for which 3 √ 3 4 r − a 1− ar 2 −a2 +4a(1−a2)r ! = 1 which may be rewritten as (10) (r − a)2 +(1− ra) 2(−a2 +4a(1− a )r) = 4 3 √ 3 (1− ar)2. Now we differentiate r in the variable a an”
- Some properties of a class of elliptic partial differential operators (2014, background): “ b) <∞. For α= 0, Heinz [17] and Colonna [14] proved the following Schwarz-Pick type estimates on planar harmonic functions, which are the following. For the related discussions on this topic, see [6, 9, 13, 19, 27]. TheoremA.([17, Lemma]) Let fbe a harmonic function of Dinto Dwith f(0) = 0. Then”