На торе длина кратчайшей нестягиваемой геодезической оценивается сверху через корень из площади тора. >> In the early 80’s, Gromov formulated several remarkable metaphors connecting the systolic inequality to important ideas in other areas of geometry. With the help of these metaphors, he proved the systolic inequality... Each metaphor gives an approach to proving the systolic inequality - a way to get started.
The goal of this essay is to explain Gromov’s metaphors... Gromov’s metaphors connect the systolic problem to the following areas:
1. General isoperimetric inequalities from geometric measure theory. (Work of Federer-Fleming, Michael-Simon, Almgren. Late 50’s to mid 80’s.)
На торе длина кратчайшей нестягиваемой геодезической оценивается сверху через корень из площади тора. >> In the early 80’s, Gromov formulated several remarkable metaphors connecting the systolic inequality to important ideas in other areas of geometry. With the help of these metaphors, he proved the systolic inequality... Each metaphor gives an approach to proving the systolic inequality - a way to get started.
The goal of this essay is to explain Gromov’s metaphors... Gromov’s metaphors connect the systolic problem to the following areas:
1. General isoperimetric inequalities from geometric measure theory. (Work of Federer-Fleming, Michael-Simon, Almgren. Late 50’s to mid 80’s.)
As the war in Ukraine rages, the messaging app Telegram has emerged as the go-to place for unfiltered live war updates for both Ukrainian refugees and increasingly isolated Russians alike. The original Telegram channel has expanded into a web of accounts for different locations, including specific pages made for individual Russian cities. There's also an English-language website, which states it is owned by the people who run the Telegram channels. Asked about its stance on disinformation, Telegram spokesperson Remi Vaughn told AFP: "As noted by our CEO, the sheer volume of information being shared on channels makes it extremely difficult to verify, so it's important that users double-check what they read." On December 23rd, 2020, Pavel Durov posted to his channel that the company would need to start generating revenue. In early 2021, he added that any advertising on the platform would not use user data for targeting, and that it would be focused on “large one-to-many channels.” He pledged that ads would be “non-intrusive” and that most users would simply not notice any change. "This time we received the coordinates of enemy vehicles marked 'V' in Kyiv region," it added.
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