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- Title
- Some uniformization problems for a fourth order conformal curvature
- KIAS Author
- Lee, Sanghoon
- Journal
- JOURNAL OF FUNCTIONAL ANALYSIS, 2025
- Archive
-
- Abstract
- In this paper, we establish the existence of conformal deformations that uniformize fourth order curvature on 4dimensional Riemannian manifolds with positive conformal invariants. Specifically, we prove that any closed, compact Riemannian manifold with positive Yamabe invariant and total Q- curvature can be conformally deformed into a metric with positive scalar curvature and constant Q- curvature. For a Riemannian manifold with umbilic boundary, positive first Yamabe invariant and total ( Q, T )-curvature, it is possible to deform it into two types of Riemannian manifolds with totally geodesic boundary and positive scalar curvature. The first type satisfies Q = constant, T = 0 while the second type satisfies Q = 0, T = constant. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.