Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds
نویسندگان
چکیده
منابع مشابه
Boundary Regularity, Uniqueness and Non-uniqueness for Ah Einstein Metrics on 4-manifolds
This paper studies several aspects of asymptotically hyperbolic Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed con...
متن کاملOn the uniqueness of Sasaki-Einstein metrics
Let S be a compact Sasakian manifold which does not admit nontrivial Hamiltonian holomorphic vector fields. If there exists an EinsteinSasakian metric on S, then it is unique.
متن کاملOn Uniqueness of Tangent Cones for Einstein Manifolds
We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section. 0. Introduction By Gromov’s compactness theo...
متن کاملLocal Existence and Uniqueness for Exterior Static Vacuum Einstein Metrics
We study solutions to the static vacuum Einstein equations on domains of the form M ' R \B with prescribed Bartnik data (γ,H) on the inner boundary ∂M . It is proved that for any smooth boundary data (γ,H) close to standard round data on the unit sphere (γ+1, 2), there exists a unique asymptotically flat solution of the static vacuum Einstein equations realizing the boundary data (γ,H) which is...
متن کاملOn the Non-uniqueness of Conformal Metrics with Prescribed Scalar and Mean Curvatures on Compact Manifolds with Boundary
For a compact Riemannian manifold (M, g) with boundary and dimension n, with n ≥ 2, we study the existence of metrics in the conformal class of g with scalar curvature Rg and mean curvature hg on the boundary. In this paper we find sufficient and necessary conditions for the existence of a smaller metric g̃ < g with curvatures Rg̃ = Rg and hg̃ = hg. Furthermore, we establish the uniqueness of such...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2003
ISSN: 0001-8708
DOI: 10.1016/s0001-8708(02)00075-0