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Nonexistence of NNSC fill-ins with large mean curvature


Author: Pengzi Miao
Journal: Proc. Amer. Math. Soc. 149 (2021), 2705-2709
MSC (2020): Primary 58J32; Secondary 53C20
DOI: https://doi.org/10.1090/proc/15400
Published electronically: March 29, 2021
MathSciNet review: 4246819
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Abstract: In this note we show that a closed Riemannian manifold does not admit a fill-in with nonnegative scalar curvature if the mean curvature is point-wise large. Similar result also holds for fill-ins with a negative scalar curvature lower bound.


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Additional Information

Pengzi Miao
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
MR Author ID: 715810
Email: pengzim@math.miami.edu

Keywords: Scalar curvature, mean curvature
Received by editor(s): September 22, 2020
Received by editor(s) in revised form: October 19, 2020
Published electronically: March 29, 2021
Additional Notes: The author’s research was partially supported by NSF grant DMS-1906423.
Communicated by: Guofang Wei
Article copyright: © Copyright 2021 American Mathematical Society