Zobrazeno 1 - 10
of 292
pro vyhledávání: '"Gover, A. Rod"'
Autor:
Dunajski, Maciej, Gover, A. Rod
We establish a one-to-one correspondence between K\"ahler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non--linear algebraic co
Externí odkaz:
http://arxiv.org/abs/2409.17347
We address the problem of how to characterise when a rank-two conformal Killing tensor is the trace-free part of a Killing tensor for a metric in the conformal class. We call such a metric a Killing scale. Our approach is via differential prolongatio
Externí odkaz:
http://arxiv.org/abs/2406.17212
Autor:
Gover, A. Rod, Wheeler, Valentina-Mira
On a manifold we term a hypersurface foliation a slicing if it is the level set foliation of a slice function -- meaning some real valued function $f$ satisfying that $df$ is nowhere zero. On Riemannian manifolds we give a non-linear PDE on functions
Externí odkaz:
http://arxiv.org/abs/2312.12796
On conformally compact manifolds we study Yang-Mills equations, their boundary conditions, formal asymptotics, and Dirichlet-to-Neumann maps. We find that smooth solutions with "magnetic" Dirichlet boundary data are obstructed by a conformally invari
Externí odkaz:
http://arxiv.org/abs/2311.11458
Publikováno v:
Phys. Rev. Lett. 133, 011401 2024
We develop the mathematics needed to treat the interaction of geometry and stress at any isotropic spacetime singularity. This enables us to handle the Einstein equations at the initial singularity and characterize allowed general relativistic stress
Externí odkaz:
http://arxiv.org/abs/2310.19269
For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a conformally
Externí odkaz:
http://arxiv.org/abs/2309.09361
Autor:
Gover, A. Rod, Gursky, Matthew J.
Let $(M^4,g)$ be a smooth, closed, oriented anti-self-dual (ASD) four-manifold. $(M^4,g)$ is said to be unobstructed if the cokernel of the linearization of the self-dual Weyl tensor is trivial. This condition can also be characterized as the vanishi
Externí odkaz:
http://arxiv.org/abs/2307.12432
We study the non-linear Dirichlet-to-Neumann map for the Poincar\'e-Einstein filling problem. For even dimensional manifolds we describe the range of this non-local map in terms of a natural rank two tensor along the boundary determined by the Poinca
Externí odkaz:
http://arxiv.org/abs/2307.08470
Autor:
Gover, A. Rod, Kopiński, Jarosław
Publikováno v:
Class. Quantum Grav. 40 015001 2023
We provide a partial characterization of the conformal infinity of asymptotically de Sitter spacetimes by deriving constraints that relate the asymptotics of the stress-energy tensor with conformal geometric data. The latter is captured using recentl
Externí odkaz:
http://arxiv.org/abs/2208.09302