The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3553–3602 | Cite as

Sewing Riemannian Manifolds with Positive Scalar Curvature

  • J. Basilio
  • J. Dodziuk
  • C. SormaniEmail author


We explore to what extent one may hope to preserve geometric properties of three-dimensional manifolds with lower scalar curvature bounds under Gromov–Hausdorff and Intrinsic Flat limits. We introduce a new construction, called sewing, of three-dimensional manifolds that preserves positive scalar curvature. We then use sewing to produce sequences of such manifolds which converge to spaces that fail to have nonnegative scalar curvature in a standard generalized sense. Since the notion of nonnegative scalar curvature is not strong enough to persist alone, we propose that one pair a lower scalar curvature bound with a lower bound on the area of a closed minimal surface when taking sequences as this will exclude the possibility of sewing of manifolds.


Scalar curvature Gromov-Hausdorff Intrinsic flat 

Mathematics Subject Classification




J. Basilio was partially supported as a doctoral student by NSF DMS 1006059. C. Sormani was partially supported by NSF DMS 1006059.


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Copyright information

© Mathematica Josephina, Inc. 2017

Authors and Affiliations

  1. 1.CUNY Graduate Center and Sarah Lawrence CollegeBronxvilleUSA
  2. 2.CUNY Graduate Center and Queens CollegeNew YorkUSA
  3. 3.CUNY Graduate Center and Lehman CollegeBronxUSA

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