Calculus of Variations and Geometric Measure Theory

L. Branca - G. Catino - D. Dameno - P. Mastrolia

Rigidity of Einstein manifolds with positive Yamabe invariant

created by catino on 17 Mar 2024
modified on 24 Mar 2025

[BibTeX]

Accepted Paper

Inserted: 17 mar 2024
Last Updated: 24 mar 2025

Journal: Ann. Glob. Anal. Geom.
Year: 2025

Abstract:

We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known bounds of the Yamabe invariant \emph{via} the $L^{\frac{n}{2}}$-norm of the Weyl tensor for low-dimensional Einstein manifolds. Finally, we discuss some advances on an algebraic inequality involving the Weyl tensor for dimensions $5$ and $6$.


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