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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.14767 |
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| _version_ | 1866918215219675136 |
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| author | Coimbra, Caio |
| author_facet | Coimbra, Caio |
| contents | In this article, we study geometric and analytical features of complete noncompact $ρ$-Einstein solitons, which are self-similar solutions of the Ricci-Bourguignon flow. We study the spectrum of the drifted Laplacian operator for complete gradient shrinking $ρ$-Einstein solitons. Moreover, similar to classical results due to Calabi--Yau and Bishop for complete Riemannian manifolds with nonnegative Ricci curvature, we prove new volume growth estimates for geodesic balls of complete noncompact $ρ$-Einstein solitons. In particular, the rigidity case is discussed. In addition, we establish weighted volume growth estimates for geodesic balls of such manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric and analytical results for $ρ$-Einstein solitons Coimbra, Caio Differential Geometry In this article, we study geometric and analytical features of complete noncompact $ρ$-Einstein solitons, which are self-similar solutions of the Ricci-Bourguignon flow. We study the spectrum of the drifted Laplacian operator for complete gradient shrinking $ρ$-Einstein solitons. Moreover, similar to classical results due to Calabi--Yau and Bishop for complete Riemannian manifolds with nonnegative Ricci curvature, we prove new volume growth estimates for geodesic balls of complete noncompact $ρ$-Einstein solitons. In particular, the rigidity case is discussed. In addition, we establish weighted volume growth estimates for geodesic balls of such manifolds. |
| title | Geometric and analytical results for $ρ$-Einstein solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.14767 |