Parametric Characteristics of High-Order Tangential Loewner’s Slits
- Autores: Prokhorov D.1,2
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Afiliações:
- Saratov State University
- Petrozavodsk State University
- Edição: Volume 39, Nº 6 (2018)
- Páginas: 818-825
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202458
- DOI: https://doi.org/10.1134/S199508021806015X
- ID: 202458
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Resumo
We describe the chordal Loewner evolution with a driving function generating the slit in the upper half-plane which is high-order tangential to the real axis at 0. In this case, the slit is a joint boundary for the analytic corner and the analytic cusp. We give an asymptotic expansion of the slit and of the conformal mapping from the upper half-plane onto the upper half-plane with the slit both in the corner and the cusp. We find also a relation between harmonic measures of the two sides of the slit.
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Sobre autores
D. Prokhorov
Saratov State University; Petrozavodsk State University
Autor responsável pela correspondência
Email: prokhorovdv@info.sgu.ru
Rússia, ul. Astrakhanskaya 83, Saratov, 410026; ul. Lenina 33, Petrozavodsk, 185000