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On lower estimations of square-linear ratio for plane Peano curvesстатья
- Авторы: Щепин Е.В., Мычка Е.Ю.
- Журнал: ArXiv e-prints
- Номер: 2103.02478v1
- Год издания: 2021
- Аннотация: It is proved that for any mapping of a unit segment to a unit square, there is a pair of points of the segment for which the square of the Euclidean distance between their images exceeds the distance between them on the segment by at least 3+5/8 times. And the additional condition that the images of the beginning and end of the segment belong to opposite sides of the square increases the estimate to 4+ε.
- Добавил в систему: Мычка Евгений Юрьевич