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REMARKS ON LOEWNER CHAINS DRIVEN BY FINITE VARIATION FUNCTIONS
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 44, p. 311-327Article in journal (Refereed) Published
Abstract [en]

To explore the relation between properties of Loewner chains and operties of their driving functions, we study Loewner chains driven by nctions U of finite total variation. Under a slow point condition, we ow the existence of a simple trace gamma and establish the continuity the map from U to gamma with respect to the uniform topology on gamma d to the total variation topology on U. In the spirit of the work of ng [19] and Lind-Tran [10], we also obtain conditions on the driving nction that ensures the trace to be continuously differentiable.

Place, publisher, year, edition, pages
SUOMALAINEN TIEDEAKATEMIA , 2019. Vol. 44, p. 311-327
Keywords [en]
Loewner differential equation, finite variation drivers, trace of Loewner chains, continuity of Loewner map
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-248109DOI: 10.5186/aasfm.2019.4421ISI: 000461094900019OAI: oai:DiVA.org:kth-248109DiVA, id: diva2:1307728
Note

QC 20190429

Available from: 2019-04-29 Created: 2019-04-29 Last updated: 2019-04-29Bibliographically approved

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