A General Nonuniqueness Result for Yamabe-Type Problems for Conformally Variational Riemannian Invariants
Abstract 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 nonhomothetic periodic conformal rescalings with I constant. Using these conditions, we improve known nonuniqueness results for the Q -curvatures of orders two, four, and six. We also prove nonuniqueness results for higher-order Q -curvatures and renormalized volume coefficients.
Authors
- João Henrique Andrade (ORCID: https://orcid.org/0000-0002-6462-3501)
- Paolo Piccione (ORCID: https://orcid.org/0000-0002-8929-5938)
- Juncheng Wei (ORCID: https://orcid.org/0000-0001-5262-477X)
- Jeffrey S. Case (ORCID: https://orcid.org/0000-0003-4972-263X)
Institutions
- Pennsylvania State University (US)
- Zhejiang Normal University (CN)
- Chinese University of Hong Kong (HK)
- Universidade de São Paulo (BR)
- Dongguan University of Technology (CN)
Publication Details
- Journal
- Journal of Geometric Analysis
- Published
- 2026-09-11
- DOI
- https://doi.org/10.1007/s12220-026-02598-4
- Citations
- 1
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Simons Foundation
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Natural Sciences and Engineering Research Council of Canada