Extremal problems of nonoverlapping domains with free poles on a circle
Let $α_1, α_2 > 0$ and let $r(B, a)$ be the interior radius of the domain $B$ lying in the extended complex plane $\overline{ℂ}$ relative to the point $a ∈ B$. In terms of quadratic differentials, we give a complete description of extremal configurations in the problem of maximization of the...
Збережено в:
| Дата: | 2006 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2006
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3503 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Let $α_1, α_2 > 0$ and let $r(B, a)$ be the interior radius of the domain $B$ lying in the extended complex plane $\overline{ℂ}$ relative to the point $a ∈ B$. In terms of quadratic differentials, we give a complete description of extremal configurations in the problem of maximization of the functional $\left( {\frac{{r(B_1 ,a_1 ) r(B_3 ,a_3 )}}{{\left| {a_1 - a_3 } \right|^2 }}} \right)^{\alpha _1 } \left( {\frac{{r(B_2 ,a_2 ) r(B_4 ,a_4 )}}{{\left| {a_2 - a_4 } \right|^2 }}} \right)^{\alpha _2 }$
defined on all collections consisting of points $a_1, a_2, a_3, a_4 ∈ \{z ∈ ℂ: |z| = 1\}$ and pairwise-disjoint domains $B_1, B_2, B_3, B_4 ⊂ \overline{ℂ}$
such that $a_1 ∈ B_1, a_1 ∈ B_2, a_3 ∈ B_3, and a_4 ∈ B_4$. |
|---|