2 citations · 4 across the 5 of their papers we have counts for
7 papers
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…
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…
Scattering on singular Yamabe spaces
Sun-Yung Alice Chang, Stephen E. McKeown, Paul Yang
We apply scattering theory on asymptotically hyperbolic manifolds to singular Yamabe metrics, applying the results to the study of the conformal geometry of compact manifolds with…
Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces
Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell
We define a renormalized volume for a region in an asymptotically hyperbolic Einstein manifold that is bounded by a Graham-Witten minimal surface and the conformal infinity. We pro…
Extrinsic curvature and conformal Gauss-Bonnet for four-manifolds with corner
Stephen E. McKeown
This paper defines two new extrinsic curvature quantities on the corner of a four-dimensional Riemannian manifold with corner. One of these is a pointwise conformal invariant, and…
Formal theory of cornered asymptotically hyperbolic Einstein metrics
Stephen E. McKeown
This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein…
Exponential map and normal form for cornered asymptotically hyperbolic metrics
Stephen E. McKeown
This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and prov…