Scalar curvature rigidity of the four-dimensional sphere
| Autor: | Cecchini, Simone, Wang, Jinmin, Xie, Zhizhang, Zhu, Bo |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $(M,g)$ be a closed connected oriented (possibly non-spin) smooth four-dimensional manifold with scalar curvature bounded below by $n(n-1)$. In this paper, we prove that if $f$ is a smooth map of non-zero degree from $(M, g)$ to the unit four-sphere, then $f$ is an isometry. Following ideas of Gromov, we use $\mu$-bubbles and a version with coefficients of the rigidity of the three-sphere to rule out the case of strict inequality. Our proof of rigidity is based on the harmonic map heat flow coupled with the Ricci flow. Comment: Improved exposition. Comments are welcome! |
| Databáze: | arXiv |
| Externí odkaz: |
|