Gluing theorem for Bakry-Emery CD(K,N) spaces under boundary conditions on second fundamental form and weight, with converse, generalizing Kosovskii.
Gluing Riemannian manifolds with curvature operators at least k
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abstract
We glue two manifolds which have curvature operators at least k (in the sense of eigenvalues) along their common boundary. We show that if the sum of the second fundamental forms of the boundary is positive semidefinite, then the curvature operator of the resulting manifold is at least k up to an arbitrarily small error term. Similar results hold for Ricci, scalar, bi, isotropic and flag curvature, respectively.
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math.DG 1years
2023 1verdicts
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Glued spaces and lower Ricci curvature bounds
Gluing theorem for Bakry-Emery CD(K,N) spaces under boundary conditions on second fundamental form and weight, with converse, generalizing Kosovskii.