27 citations · 35 across the 20 of their papers we have counts for
11 papers · 1 filter
Potential Carroll Structures and Special Carrollian Manifolds
Samuel Blitz, Gabriel Herczeg, David McNutt
It is well-known that unlike space-like and time-like hypersurfaces, null hypersurfaces in Lorentzian manifolds do not naturally inherit an affine connection from the spacetime in…
Einstein and Yang-Mills implies conformal Yang-Mills
Samuel Blitz, A. Rod Gover, Jarosław Kopiński +1
There exist conformally invariant, higher-derivative, variational analogs of the Yang-Mills condition for connections on vector bundles over a conformal manifold of even dimension…
Conformal hypersurface invariants and Bach-type Boundary Problems
Samuel Blitz, A. Rod Gover
Using variational considerations, we establish that there exists a new symmetric trace-free tensor conformal invariant of hypersurfaces embeddings in even dimensional conformal man…
Non-existence of higher-order conformal fundamental forms in odd dimensions
Samuel Blitz
Conformal fundamental forms populate a minimal generating set for low differential order invariants of conformal hypersurface embeddings. In this work we complete the characterizat…
Higher Fundamental Forms and Warped Product Hypersurfaces
Samuel Blitz, Josef Silhan
Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddi…
Holography of Higher Codimension Submanifolds: Riemannian and Conformal
Samuel Blitz, Josef Šilhan
We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of whi…
The Dirichlet-to-Neumann Map for Poincaré-Einstein Fillings
Samuel Blitz, A. Rod Gover, Jarosław Kopiński +1
We study the non-linear Dirichlet-to-Neumann map for the Poincaré-Einstein filling problem. For even dimensional manifolds the range of this non-local map is described in terms of…
Toward a Classification of Conformal Hypersurface Invariants
Samuel Blitz
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinit…
A Sharp Characterization of the Willmore Invariant
Samuel Blitz
First introduced to describe surfaces embedded in , the Willmore invariant is a conformally-invariant extrinsic scalar curvature of a surface that vanishes when the s…
Generalized Willmore Energies, Q-Curvatures, Extrinsic Paneitz Operators, and Extrinsic Laplacian Powers
Samuel Blitz, A. Rod Gover, Andrew Waldron
Over forty years ago, Paneitz, and independently Fradkin and Tseytlin, discovered a fourth-order conformally-invariant differential operator, intrinsically defined on a conformal m…
Conformal Fundamental Forms and the Asymptotically Poincaré--Einstein Condition
Samuel Blitz, A. Rod Gover, Andrew Waldron
An important problem is to determine under which circumstances a metric on a conformally compact manifold is conformal to a Poincaré--Einstein metric. Such conformal rescalings are…