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

Abstract

We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries

arXiv commentWe sharpen the main result and simplify the proof from the earlier version of this paper

Cited by in corpus (10)

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• Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces
• On the Fill-in of Nonnegative Scalar Curvature Metrics
• NNSC-Cobordism of Bartnik Data in High Dimensions
• Nonexistence of NNSC fill-ins with large mean curvature
• Rigidity and Non-Rigidity of ${\mathbb{H}}^n/{\mathbb{Z}}^{n-2}$ with Scalar Curvature Bounded from Below
• Covariant vs Contravariant Methods in Differential Geometry
• Nonexistence of DEC spin fill-ins
• Nonexistence of NNSC-cobordism of Bartnik data
• A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary