The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II)
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912025403195392 |
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| author | Li, Mingxiang |
| author_facet | Li, Mingxiang |
| contents | This is a continuation of our previous work (Advances in Mathematics 450 (2024), Paper No. 109768). In this paper, we characterize complete metrics with finite total Q-curvature as normal metrics for all dimensional cases. Secondly, we introduce another volume entropy to provide geometric information regarding complete non-normal metrics with finite total Q-curvature. In particular, we show that if the scalar curvature is bounded from below, the volume growth of such complete metrics is controlled. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_03640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II) Li, Mingxiang Differential Geometry Analysis of PDEs 53C18, 58J90 This is a continuation of our previous work (Advances in Mathematics 450 (2024), Paper No. 109768). In this paper, we characterize complete metrics with finite total Q-curvature as normal metrics for all dimensional cases. Secondly, we introduce another volume entropy to provide geometric information regarding complete non-normal metrics with finite total Q-curvature. In particular, we show that if the scalar curvature is bounded from below, the volume growth of such complete metrics is controlled. |
| title | The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II) |
| topic | Differential Geometry Analysis of PDEs 53C18, 58J90 |
| url | https://arxiv.org/abs/2408.03640 |