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math.DG2026

Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities

Mitchell Gaudet

In this paper, we use optimal mass transportation to derive an isoperimetric inequality and an interior Michael-Simon-Sobolev inequality for weakly twice differentiable integral va…

math.DG2026

Morse index of min-max stationary integral varifolds

Mitchell Gaudet, Talant Talipov

We prove an upper bound for the Morse index of min-max stationary integral varifolds realizing the -dimensional -width of a closed Riemannian manifold.