Zobrazeno 1 - 10
of 19
pro vyhledávání: '"McKeown, Stephen E."'
Given an embedded closed submanifold $\Sigma^n$ in the closed Riemannian manifold $M^{n + k}$, where $k < n + 2$, we define extrinsic global conformal invariants of $\Sigma$ by renormalizing the volume associated to the unique singular Yamabe metric
Externí odkaz:
http://arxiv.org/abs/2408.01882
We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of the boundary
Externí odkaz:
http://arxiv.org/abs/2407.08851
We show that the half-ball in $\mathbb{R}^4$ can be conformally changed so that the only contribution to the Gauss--Bonnet formula is a constant term at the corner. This may be seen as a fourth-order Cherrier--Escobar-type problem on the half-ball.
Externí odkaz:
http://arxiv.org/abs/2401.00937
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 boundary. In particular, we define extrinsic versions of the conformal
Externí odkaz:
http://arxiv.org/abs/2109.02014
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 prove a Gauss-Bonnet theorem for the renormalized volume, and compute its
Externí odkaz:
http://arxiv.org/abs/2101.11755
Autor:
McKeown, Stephen E.
Publikováno v:
Pacific J. Math. 314 (2021) 411-424
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 the conformal transformation of the other is governed by a new linear
Externí odkaz:
http://arxiv.org/abs/2010.07502
Autor:
McKeown, Stephen E.
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 metric exists thus has a finite boundary in addition to the usual infi
Externí odkaz:
http://arxiv.org/abs/1708.02390
Publikováno v:
Notices of the American Mathematical Society; Aug2024, Vol. 71 Issue 7, p878-883, 6p
Autor:
McKeown, Stephen E.
This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the normal expo
Externí odkaz:
http://arxiv.org/abs/1609.09590
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