Determines infinitesimal structure at boundary singular points and Hausdorff dimensions of boundary singular sets in limits of manifolds with boundary under sectional curvature, second fundamental form, and diameter bounds when inradii are bounded below.
Self and partial gluing theorems for Alexandrov spaces with a lower curvature bound
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abstract
This paper is devoted to prove that if an Alexandrov space of curvature not less than $\kappa$ with a codimension one extremal subset which admits an isometric involution with respect to the induced length metric, then the metric space obtained by gluing the extremal subset along the isometry is an Alexandrov space of curvature not less than $\kappa$. This is a generalization of Perelman's doubling and Petrunin's gluing theorems.
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math.DG 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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Limits of manifolds with boundary I
Determines infinitesimal structure at boundary singular points and Hausdorff dimensions of boundary singular sets in limits of manifolds with boundary under sectional curvature, second fundamental form, and diameter bounds when inradii are bounded below.