Convergence of the Yamabe flow on singular spaces with positive Yamabe constant
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866911115010637824 |
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| author | Carron, Gilles Lye, Jørgen Olsen Vertman, Boris |
| author_facet | Carron, Gilles Lye, Jørgen Olsen Vertman, Boris |
| contents | In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low energy condition. We also prove a concentration - compactness dichotomy, and investigate what the alternatives to convergence are. We end by investigating a non-convergent example due to Viaclovsky in more detail. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2106_01799 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Convergence of the Yamabe flow on singular spaces with positive Yamabe constant Carron, Gilles Lye, Jørgen Olsen Vertman, Boris Differential Geometry Analysis of PDEs 53C44, 58J35, 35K08 In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low energy condition. We also prove a concentration - compactness dichotomy, and investigate what the alternatives to convergence are. We end by investigating a non-convergent example due to Viaclovsky in more detail. |
| title | Convergence of the Yamabe flow on singular spaces with positive Yamabe constant |
| topic | Differential Geometry Analysis of PDEs 53C44, 58J35, 35K08 |
| url | https://arxiv.org/abs/2106.01799 |