Free Boundary Stable Minimal Hypersurfaces in Positively Curved 4-Manifolds
Yujie Wu
TL;DR
This paper establishes rigidity results for free boundary stable minimal hypersurfaces in 4-manifolds with positive curvature conditions, extending existing methods to manifolds with boundary.
Contribution
It extends the method of Chodosh-Li-Stryker to free boundary minimal hypersurfaces in 4-manifolds with boundary under curvature conditions.
Findings
Rigidity of free boundary stable minimal hypersurfaces under curvature assumptions
Extension of existing methods to manifolds with boundary
Conditions involving nonnegative 2-intermediate Ricci curvature and scalar positivity
Abstract
We show that the combination of nonnegative 2-intermediate Ricci Curvature and strict positivity of scalar curvature forces rigidity of two-sided free boundary stable minimal hypersurface in a 4-manifold with bounded geometry and weakly convex boundary. This extends the method of Chodosh-Li-Stryker to free boundary minimal hypersurfaces in ambient manifolds with boundary.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds