Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 136, 7 pages      arXiv:2007.02705
Contribution to the Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday

On the 2-Systole of Stretched Enough Positive Scalar Curvature Metrics on $\mathbb{S}^2\times\mathbb{S}^2$

Thomas Richard ab
a) Univ Paris Est Creteil, CNRS, LAMA, F-94010 Creteil, France
b) Univ Gustave Eiffel, LAMA, F-77447 Marne-la-Vallée, France

Received July 07, 2020, in final form December 14, 2020; Published online December 17, 2020

We use recent developments by Gromov and Zhu to derive an upper bound for the 2-systole of the homology class of $\mathbb{S}^2\times\{\ast\}$ in a $\mathbb{S}^2\times\mathbb{S}^2$ with a positive scalar curvature metric such that the set of surfaces homologous to $\mathbb{S}^2\times\{\ast\}$ is wide enough in some sense.

Key words: scalar curvature; higher systoles; geometric inequalities.

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