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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Minimize Perimeter(S)/Area(S) for S inside the unit square.
This is a very silly question.
For all regions S contained inside the unit square, what is the infimum of the quantity Perimeter(S)/Area(S)? This ratio being considered is not scale invariant, so it …