Linear and nonlinear stability for the Bach flow, I
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911100279193600 |
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| author | Bahuaud, Eric Guenther, Christine Isenberg, James Mazzeo, Rafe |
| author_facet | Bahuaud, Eric Guenther, Christine Isenberg, James Mazzeo, Rafe |
| contents | In this paper we prove the linear stability of a gauge-modified version of the Bach flow on any complete manifold (M, h) of constant curvature. This involves some intricate calculations to obtain spectral bounds, and in particular introduces a higher order generalization of the well-known Koiso identity. We also prove nonlinear stability for the Bach flow if (M, h) is hyperbolic space, and more generally any Poincaré-Einstein space sufficiently close to h. In the forthcoming Part II of this project, we study the nonlinear stability question if M is either compact or else noncompact and flat, since those cases require different considerations involving a center manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear and nonlinear stability for the Bach flow, I Bahuaud, Eric Guenther, Christine Isenberg, James Mazzeo, Rafe Differential Geometry Analysis of PDEs 58J35, 53E40, 35K In this paper we prove the linear stability of a gauge-modified version of the Bach flow on any complete manifold (M, h) of constant curvature. This involves some intricate calculations to obtain spectral bounds, and in particular introduces a higher order generalization of the well-known Koiso identity. We also prove nonlinear stability for the Bach flow if (M, h) is hyperbolic space, and more generally any Poincaré-Einstein space sufficiently close to h. In the forthcoming Part II of this project, we study the nonlinear stability question if M is either compact or else noncompact and flat, since those cases require different considerations involving a center manifold. |
| title | Linear and nonlinear stability for the Bach flow, I |
| topic | Differential Geometry Analysis of PDEs 58J35, 53E40, 35K |
| url | https://arxiv.org/abs/2508.06633 |