Warped Tori with Almost Non-Negative Scalar Curvature

Brian Allen; Lisandra Hernandez-Vazquez; Davide Parise; Alec Payne; Shengwen Wang

doi:10.1007/s10711-018-0365-y

Warped Tori with Almost Non-Negative Scalar Curvature

Differential Geometry 2023-06-27 v4 Metric Geometry

Authors: Brian Allen , Lisandra Hernandez-Vazquez , Davide Parise , Alec Payne , Shengwen Wang

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Abstract

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.

Keywords

warped product metrics scalar curvature 3-torus gromov-hausdorff convergence intrinsic flat convergence minimal surface volume bound

Cite

@article{arxiv.1804.04581,
  title  = {Warped Tori with Almost Non-Negative Scalar Curvature},
  author = {Brian Allen and Lisandra Hernandez-Vazquez and Davide Parise and Alec Payne and Shengwen Wang},
  journal= {arXiv preprint arXiv:1804.04581},
  year   = {2023}
}

Comments

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

Warped Tori with Almost Non-Negative Scalar Curvature

Abstract

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