Of Waists and Spheres

These are some notes that I’m writing up on Gromov‘s waist inequality. We’ll look at some standard material about the Borsuk-Ulam theorem and finish with a nice application of the inequality.

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The Spherical Isoperimetric Inequality

Here is an application of the spherical isoperimetric inequality.

Fact You can’t cut up a beach ball into equal parts with a path that is too short.