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math.DG2019
The Riemannian Quantitative Isoperimetric Inequality
Otis Chodosh, Max Engelstein, Luca Spolaor
We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed…
math.DG2009
The Least-Perimeter Partition of a Sphere into Four Equal Areas
Max Engelstein
We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.