Calculus of Variations and Geometric Measure Theory

B. Allen - L. Hernandez-Vazquez - D. Parise - A. Payne - S. Wang

Warped Tori with Almost Non-Negative Scalar Curvature

created by wang on 13 Nov 2020


Published Paper

Inserted: 13 nov 2020
Last Updated: 13 nov 2020

Journal: Geometriae Dedicata
Volume: 200
Pages: 153-171
Year: 2018

ArXiv: 1804.04581 PDF


For sequences of warped product metrics on a $3$-torus satisfying the scalar curvature bound $R_j \geq -\frac{1}{j}$, uniform upper volume and diameter bounds, and a uniform lower area bound on the smallest minimal surface, we find a subsequence which converges in both the Gromov-Hausdorff and the Sormani-Wenger Intrinsic Flat sense to a flat $3$-torus.