A General Nonuniqueness Result for Yamabe-Type Problems for Conformally Variational Riemannian Invariants

Journal of Geometric Analysis 2026 Open access

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Authors: João Henrique Andrade, Jeffrey S. Case, Paolo Piccione, Juncheng Wei
DOI: 10.1007/s12220-026-02598-4
Cited by: 1
References: 43

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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Nonlinear Partial Differential Equations Analytic and geometric function theory

Publication details

Journal / source
Journal of Geometric Analysis
Publisher
Springer Science and Business Media LLC
Volume
36
Issue
11
Pages
352–352
Publication date
11 September 2026
Language
EN