ON TANGENTIAL SLIT SOLUTION OF THE LOEWNER EQUATION
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AbstractFor a non-tangential slit gamma(t), the behavior of the driving function lambda(t) near zero in the Loewner equation is well understood; for tangential slit, the situation is less clear. In this paper, we investigate the tangential slit Gamma(p), p > 0, where I' is a circular arc tangent at 0; Gamma(p) has order p+1/p near zero. Our main result is to give the exact expression of lambda(t), and its Holder exponent near 0 in terms of p, which has a natural connection with the known results. We also extend this to a general type of tangential slits, and give an estimation of the growth of lambda(t) near 0.
All Author(s) ListLau KS, Wu HH
Journal nameAnnales Academiae Scientiarum Fennicae. Mathematica
Year2016
Month1
Day1
Volume Number41
Issue Number2
PublisherSUOMALAINEN TIEDEAKATEMIA
Pages681 - 691
ISSN1798-2383
eISSN1798-2383
LanguagesEnglish-United Kingdom
Keywordsdriving function; half-plane capacity; hull; Loewner equation; trace
Web of Science Subject CategoriesMathematics

Last updated on 2021-25-01 at 02:15