A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911275777261568 |
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| author | Bieganowski, Bartosz d'Avenia, Pietro Schino, Jacopo Strzelecki, Daniel |
| author_facet | Bieganowski, Bartosz d'Avenia, Pietro Schino, Jacopo Strzelecki, Daniel |
| contents | In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-constant mean curvature. In particular, the non-constant mean curvature gives rise to supercritical terms in the equation, on top of singular ones. We employ a recent fixed-point argument, which involves sub- and supersolutions. Additionally, we provide several conditions on the coefficients in the equation that prevent the existence of positive classical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds Bieganowski, Bartosz d'Avenia, Pietro Schino, Jacopo Strzelecki, Daniel Analysis of PDEs Mathematical Physics Differential Geometry In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-constant mean curvature. In particular, the non-constant mean curvature gives rise to supercritical terms in the equation, on top of singular ones. We employ a recent fixed-point argument, which involves sub- and supersolutions. Additionally, we provide several conditions on the coefficients in the equation that prevent the existence of positive classical solutions. |
| title | A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2510.17669 |