Curvature Deformations on Complete Manifolds with Boundary
Tiarlos Cruz, Almir Silva Santos
TL;DR
This paper studies how to deform the scalar and mean curvature conformally on complete manifolds with boundary, providing conditions for achieving positive curvature metrics and exploring various deformation scenarios.
Contribution
It establishes new sufficient conditions for conformal deformations to complete metrics with positive scalar and mean curvature, extending to negative scalar curvature cases.
Findings
Conditions for conformal deformations to positive scalar curvature
Methods for increasing mean curvature through deformation
Analysis of negative scalar curvature deformations on noncompact boundaries
Abstract
This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics with positive scalar curvature and mean convex boundary. Building upon these results, we explore further deformation scenarios, including those that increase the mean curvature. Finally, we consider the case of deforming complete manifolds with negative scalar curvature on manifolds with noncompact boundary.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology