The RCD gluing conjecture along intrinsic boundaries

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Let X0X_0 and X1X_1 be noncollapsed RCD(K,n)RCD(K,n) spaces with nonempty boundaries ∂X0\partial X_0 and ∂X1\partial X_1, where the boundaries are understood in the sense of Gigli and Pasqualetto. Suppose there is an isometry

I:∂X0→∂X1\mathcal I:\partial X_0\rightarrow \partial X_1

with respect to their induced intrinsic metrics. RCD gluing conjecture. The glued metric measure space (X0∪IX1,HX0∪IX1n)(X_0\cup_{\mathcal I}X_1,\mathcal H^n_{X_0\cup_{\mathcal I}X_1}) satisfies RCD(K,n)RCD(K,n). This conjecture seeks a generalization of Petrunin's gluing theorem to noncollapsed RCDRCD spaces; its resolution is not established by the supplied text.

References

Primary source

Christian Ketterer, “Glued spaces and lower curvature bounds”, arXiv:2408.13137 (2026).

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