Scalar Curvature of Manifolds with Boundaries: Natural Questions and Artificial Constructions
Misha Gromov
TL;DR
This paper explores the scalar curvature of manifolds with boundaries, addressing natural questions and introducing artificial constructions to analyze how boundary mean curvature influences scalar curvature properties.
Contribution
It presents new problems, results, and constructions that deepen understanding of scalar curvature behavior in manifolds with boundary.
Findings
Identifies key problems relating scalar and boundary mean curvatures
Provides new constructions demonstrating scalar curvature phenomena
Offers results connecting boundary conditions with scalar curvature properties
Abstract
We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research