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math.DG2024
Volume Above Distance Below with Boundary II
Brian Allen, Edward Bryden
It was shown by B. Allen, R. Perales, and C. Sormani that on a closed manifold where the diameter of a sequence of Riemannian metrics is bounded, if the volume converges to the vol…
math.DG2024
On the Scalar Curvature Compactness Conjecture in the Conformal Case
Brian Allen, Wenchuan Tian, Changliang Wang
Is a sequence of Riemannian manifolds with positive scalar curvature, satisfying some conditions to keep the sequence reasonable, compact? What topology should one use for the conv…