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math.DG2024
Volume renormalization of higher-codimension singular Yamabe spaces
Sri Rama Chandra Kushtagi, Stephen E. McKeown
Given an embedded closed submanifold in the closed Riemannian manifold , where , we define extrinsic global conformal invariants of by renormalizing…
math.DG2024
Self-dual and even Poincaré-Einstein metrics in dimension four
Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell
We prove rigidity and gap theorems for self-dual and even Poincaré-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré…