A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918155687821312 |
|---|---|
| author | Andrade, João Henrique Case, Jeffrey S. Piccione, Paolo Wei, Juncheng |
| author_facet | Andrade, João Henrique Case, Jeffrey S. Piccione, Paolo Wei, Juncheng |
| contents | Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also identify a sufficient condition for the universal cover to admit infinitely many geometrically distinct periodic conformal rescalings with $I$ constant. Using these conditions, we improve known nonuniqueness results for the $Q$-curvatures of orders two, four, and six, and establish nonuniqueness results for higher-order $Q$-curvatures and renormalized volume coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15798 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants Andrade, João Henrique Case, Jeffrey S. Piccione, Paolo Wei, Juncheng Differential Geometry Analysis of PDEs Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also identify a sufficient condition for the universal cover to admit infinitely many geometrically distinct periodic conformal rescalings with $I$ constant. Using these conditions, we improve known nonuniqueness results for the $Q$-curvatures of orders two, four, and six, and establish nonuniqueness results for higher-order $Q$-curvatures and renormalized volume coefficients. |
| title | A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2310.15798 |