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On regularity of a quasiconformal mapping at a point of maximal stretching
Author(s) -
Gutlyanskiĭ Vladimir Ya.,
Martio Olli
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm022
Subject(s) - mathematics , point (geometry) , limit (mathematics) , mathematical analysis , quasiconformal mapping , combinatorics , pure mathematics , geometry
Local behaviour of a K ‐quasiconformal mapping f at a point z 0 of maximal stretching is studied. A sufficient condition for the existence of the finite limit lim( f ( z ) − f ( z 0 ))/( z − z 0 )| z − z 0 | 1/ K −1 as z → z 0 , and a criterion for z 0 to be a point of maximal stretching are given.