|
ИСТИНА |
Войти в систему Регистрация |
ИПМех РАН |
||
Fermat-Steiner Problem in the Metric Space of Compact Setsтезисы доклада Тезисы
- Автор: Ivanov A.O.
- Сборник: 4th International Workshop ``Analysis, Geometry, and Probability'', Book of Abstracts
- Тезисы
- Год издания: 2016
- Издательство: Izdatel'stvo Moskovskogo Gosudarstvennogo Universiteta im.M.V.Lomonosova/Publishing House of Moscow State University
- Местоположение издательства: Russian Federation
- Первая страница: 8
- Последняя страница: 9
- Аннотация: Fermat--Steiner problem consists in finding all points in a metric space $Y$ such that the sum of distances from each of them to the points from some fixed finite subset of $Y$ is minimal. This problem is investigated for the metric space $Y=H(X)$ of compact subsets of a metric space $X$, endowed with the Hausdorff distance. For the case of a proper metric space $X$ a description of all compacts $K\in H(X)$ which the minimum is attained at is obtained. In particular, the Steiner minimal trees for three-element boundaries are described. We also construct an example of a regular triangle in $H(\R^2)$, such that all its shortest trees have no ``natural'' symmetry.
- Добавил в систему: Иванов Александр Олегович