Scalar Curvature of Manifolds with Boundaries: Natural Questions and Artificial Constructions

Key Points

• The aim is to explore various problems concerning scalar curvatures and the mean curvatures of boundaries in manifold structures.
• Examined several problems related to scalar and mean curvatures in mathematical manifolds.
• Utilized various theoretical frameworks and constructions to analyze curvature behavior.
• Identified new relationships between scalar curvature and boundary mean curvature.
• Presented results indicating potential implications for geometric analysis and manifold theory.