Journal of Geometric Analysis· 2026Q1
A General Nonuniqueness Result for Yamabe-Type Problems for Conformally Variational Riemannian Invariants
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- Q1SCImago
- 2026year
Short summary
Researchers identified conditions for compact Riemannian manifolds to have many nonhomothetic conformal rescalings with constant scalar invariants, improving nonuniqueness results for Q-curvatures and renormalized volume coefficients.
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Key points
- Identified sufficient conditions for compact Riemannian manifolds to have numerous nonhomothetic conformal rescalings with constant scalar invariants.
- Provided sufficient conditions for universal covers to admit infinitely many periodic conformal rescalings with constant scalar invariants.
- Improved known nonuniqueness results for Q-curvatures of orders two, four, and six.
- Proved new nonuniqueness results for higher-order Q-curvatures and renormalized volume coefficients.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Journal of Geometric Analysis, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics