Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary
We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar c...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022064?viewType=HTML |
| _version_ | 1811250407729528832 |
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| author | Marco G. Ghimenti Anna Maria Micheletti |
| author_facet | Marco G. Ghimenti Anna Maria Micheletti |
| author_sort | Marco G. Ghimenti |
| collection | DOAJ |
| description | We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature with a function with a large positive maximum. |
| first_indexed | 2024-04-12T16:04:14Z |
| format | Article |
| id | doaj.art-370710cfb98b4a6a96e2d9be5cdab351 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T16:04:14Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-370710cfb98b4a6a96e2d9be5cdab3512022-12-22T03:26:07ZengAIMS PressElectronic Research Archive2688-15942022-03-013041209123510.3934/era.2022064Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundaryMarco G. Ghimenti0Anna Maria Micheletti 1Dipartimento di Matematica Università di Pisa Largo B. Pontecorvo 5, 56126 Pisa, ItalyDipartimento di Matematica Università di Pisa Largo B. Pontecorvo 5, 56126 Pisa, ItalyWe study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature with a function with a large positive maximum.https://www.aimspress.com/article/doi/10.3934/era.2022064?viewType=HTMLnon umbilic boundaryyamabe problemcompactnessblow up analysis |
| spellingShingle | Marco G. Ghimenti Anna Maria Micheletti Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary Electronic Research Archive non umbilic boundary yamabe problem compactness blow up analysis |
| title | Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary |
| title_full | Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary |
| title_fullStr | Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary |
| title_full_unstemmed | Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary |
| title_short | Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary |
| title_sort | compactness and blow up results for doubly perturbed yamabe problems on manifolds with non umbilic boundary |
| topic | non umbilic boundary yamabe problem compactness blow up analysis |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022064?viewType=HTML |
| work_keys_str_mv | AT marcogghimenti compactnessandblowupresultsfordoublyperturbedyamabeproblemsonmanifoldswithnonumbilicboundary AT annamariamicheletti compactnessandblowupresultsfordoublyperturbedyamabeproblemsonmanifoldswithnonumbilicboundary |