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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.04121 |
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| _version_ | 1866909337056706560 |
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| author | Das, Anushree Maity, Soma |
| author_facet | Das, Anushree Maity, Soma |
| contents | Let $M$ be an open manifold of dimension at least $3$, which admits a complete metric of positive scalar curvature. For a function $v$ with bounded growth of derivative, whether $M$ admits a metric of positive scalar curvature with volume growth of the same growth type as $v$ is unknown. We answer this question positively in the case of manifolds, which are infinite connected sums of closed manifolds that admit metrics of positive scalar curvature. To define a metric of positive scalar curvature with a certain volume growth type on $M$, we use the Gromov-Lawson construction of metrics with positive scalar curvature on connected sums and Grimaldi-Pansu's construction of metrics of bounded geometry of certain volume growth type on open manifolds. We generalize this result to manifolds, which are infinite connected sums of similar closed manifolds along lower-dimensional spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Volume growth functions of complete Riemannian manifolds with positive scalar curvature Das, Anushree Maity, Soma Differential Geometry 53C20 (Primary), 53C21, 53C23 (Secondary) Let $M$ be an open manifold of dimension at least $3$, which admits a complete metric of positive scalar curvature. For a function $v$ with bounded growth of derivative, whether $M$ admits a metric of positive scalar curvature with volume growth of the same growth type as $v$ is unknown. We answer this question positively in the case of manifolds, which are infinite connected sums of closed manifolds that admit metrics of positive scalar curvature. To define a metric of positive scalar curvature with a certain volume growth type on $M$, we use the Gromov-Lawson construction of metrics with positive scalar curvature on connected sums and Grimaldi-Pansu's construction of metrics of bounded geometry of certain volume growth type on open manifolds. We generalize this result to manifolds, which are infinite connected sums of similar closed manifolds along lower-dimensional spheres. |
| title | Volume growth functions of complete Riemannian manifolds with positive scalar curvature |
| topic | Differential Geometry 53C20 (Primary), 53C21, 53C23 (Secondary) |
| url | https://arxiv.org/abs/2410.04121 |