ABSTRACT
This research proposes a framework to investigate scalar curvature rigidity in non-locally conformally flat 4-manifolds, addressing a gap in conformal geometry and introducing a curvature regularization scheme.
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Key findings
Proposes a novel curvature regularization scheme combining Bach-flatness with Weyl tensor constraints.
Establishes new rigidity criteria for 4-dimensional Riemannian manifolds with non-trivial Weyl curvature.
Introduces a comprehensive methodology integrating geometric analysis and elliptic PDE methods.
Limitations & open questions
Focuses primarily on theoretical development; computational tools and validation are in developmental stages.