Warped Tori with Almost Non-Negative Scalar Curvature

Abstract

For sequences of warped product metrics on a $3$-torus satisfying the scalar curvature bound $R_j\ge -\frac{1}{j}$, 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.

15 pages. We correct and simplify the argument for Theorem 0.3. The statements of the main theorems have not changed

References in corpus (1)

• Contrasting Various Notions of Convergence in Geometric Analysis

Cited by in corpus (3)

• Almost non-negative scalar curvature on Riemannian manifolds conformal to tori
• Contrasting Various Notions of Convergence in Geometric Analysis
• Sobolev Inequalities and Convergence For Riemannian Metrics and Distance Functions