tropical saint petersburg

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.)

2. Topological dimension theory. (Work of Brouwer, Lebesgue, Szpilrajn. 1900- 1940.)

3. Scalar curvature. (Work of Schoen-Yau. Late 70’s.)

4. Hyperbolic geometry and topological complexity. (Work of Thurston-Milnor. Late 70’s.)

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7.3K viewsedited  Dec 25, 2023 at 05:47

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.)

2. Topological dimension theory. (Work of Brouwer, Lebesgue, Szpilrajn. 1900- 1940.)

3. Scalar curvature. (Work of Schoen-Yau. Late 70’s.)

4. Hyperbolic geometry and topological complexity. (Work of Thurston-Milnor. Late 70’s.)

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