Barycenter technique for the higher order $Q$-curvature equation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914375310245888 |
|---|---|
| author | Mazumdar, Saikat Ndiaye, Cheikh Birahim |
| author_facet | Mazumdar, Saikat Ndiaye, Cheikh Birahim |
| contents | Let $k\ge1$ be an integer, and $(M,g)$ be a smooth, closed Riemannian manifold of dimension $2k+1\le n\le 2k+3$, or $(M,g)$ be locally conformally flat of dimension $n\ge 2k+1$.
Applying the Bahri-Coron barycenter method, we show the existence of a conformal metric with constant $Q$-curvature of order $2k$, or equivalently, the existence of a positive solution for the $2k$-th order $Q$-curvature equation involving the GJMS operator $P_{g}$. We only assume a natural positivity preserving condition on $P_{g}$ and do not suppose any condition on the sign of the {\emph{mass}} of $P_{g}$. In particular, we obtain existence without using a positive mass theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06249 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Barycenter technique for the higher order $Q$-curvature equation Mazumdar, Saikat Ndiaye, Cheikh Birahim Differential Geometry Analysis of PDEs Let $k\ge1$ be an integer, and $(M,g)$ be a smooth, closed Riemannian manifold of dimension $2k+1\le n\le 2k+3$, or $(M,g)$ be locally conformally flat of dimension $n\ge 2k+1$. Applying the Bahri-Coron barycenter method, we show the existence of a conformal metric with constant $Q$-curvature of order $2k$, or equivalently, the existence of a positive solution for the $2k$-th order $Q$-curvature equation involving the GJMS operator $P_{g}$. We only assume a natural positivity preserving condition on $P_{g}$ and do not suppose any condition on the sign of the {\emph{mass}} of $P_{g}$. In particular, we obtain existence without using a positive mass theorem. |
| title | Barycenter technique for the higher order $Q$-curvature equation |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2603.06249 |