Quantitative $W^{2, p}$-stability for almost Einstein hypersurfaces
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- by Stefano Gioffrè PDF
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Abstract:
Let $n \ge 3$, $p \in (1, +\infty )$ be given. Let $\Sigma$ be an $n$-dimensional, closed hypersurface in $\mathbb {R}^{n+1}$. It is a well known fact that if $\Sigma$ is an Einstein hypersurface with positive scalar curvature, then it is a round sphere. Here we prove that if a hypersurface is almost Einstein in an $L^p$-sense, then it is $W^{2, p}$-close to a sphere and we give a quantitative version of this fact.References
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Additional Information
- Stefano Gioffrè
- Affiliation: Institut für Mathematik, Universität Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
- Email: stefano.gioffre@math.uzh.ch
- Received by editor(s): April 10, 2017
- Received by editor(s) in revised form: September 29, 2017
- Published electronically: December 3, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 3505-3528
- MSC (2010): Primary 53-XX, 58-XX
- DOI: https://doi.org/10.1090/tran/7504
- MathSciNet review: 3896120