We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with () and, respectively, compact boundary is bi-Lipschitz. This theorem extends a similar result of the author [10] for Jordan domains, where stronger boundary conditions for the image domain were needed. The proof uses distance function from the boundary of the image domain.
@article{ASNSP_2011_5_10_3_669_0, author = {Kalaj, David}, title = {Harmonic mappings and distance function}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {669--681}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 10}, number = {3}, year = {2011}, mrnumber = {2905382}, zbl = {1252.30018}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2011_5_10_3_669_0/} }
TY - JOUR AU - Kalaj, David TI - Harmonic mappings and distance function JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 669 EP - 681 VL - 10 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_3_669_0/ LA - en ID - ASNSP_2011_5_10_3_669_0 ER -
Kalaj, David. Harmonic mappings and distance function. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 3, pp. 669-681. http://www.numdam.org/item/ASNSP_2011_5_10_3_669_0/
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