Metric limits of manifolds with positive scalar curvature

Key Points

• This research explores the limits of Riemannian metrics conformal to the round metric on spheres with positive scalar curvature.
• Demonstrated sequence of Riemannian metrics on spheres for n ≥ 4
• Analyzed uniform convergence of Riemannian distance
• Assessed non-negativity preservation of scalar curvature under limits
• Validated that all conformal metrics on S^n arise from limits of positive scalar curvature metrics
• Established that non-negativity of scalar curvature is not maintained through metric limits