Uniqueness of critical metrics for a quadratic curvature functional
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916557146292224 |
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| author | Catino, Giovanni Mastrolia, Paolo Monticelli, Dario D. |
| author_facet | Catino, Giovanni Mastrolia, Paolo Monticelli, Dario D. |
| contents | In this paper we prove a new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functional $\mathfrak{S}^2 = \int R_g^{2} dV_g$: we show that critical metrics $(M^n, g)$ with finite energy are always scalar flat, i.e. global minima, provided $n\geq 10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08025 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniqueness of critical metrics for a quadratic curvature functional Catino, Giovanni Mastrolia, Paolo Monticelli, Dario D. Differential Geometry In this paper we prove a new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functional $\mathfrak{S}^2 = \int R_g^{2} dV_g$: we show that critical metrics $(M^n, g)$ with finite energy are always scalar flat, i.e. global minima, provided $n\geq 10$. |
| title | Uniqueness of critical metrics for a quadratic curvature functional |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2303.08025 |