arXiv research

Paper proves uniqueness and existence of CCE metrics with homogeneous conformal infinity.

The paper proves uniqueness and existence of CCE metrics with specific conformal infinities.

Paper proves uniqueness of conformally compact Einstein metrics with specific conformal infinity.

Study spin-0 fields on n-dimensional Minkowski spacetimes, computing asymptotic charges.

New spaces at infinity identified for Minkowski spacetime.

On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bu…

Study BGG operators on homogeneous conformal geometries.

The study proves rigidity for Poincaré-Einstein manifolds with flat Euclidean conformal infinity.

Study geodesics in conformally compact manifolds, showing smoothness and asymptotic behavior.

In this paper, we give a sharp spectral characterization of conformally compact Einstein manifolds with conformal infinity of positive Yamabe type in dimension $n+1>3$. More precisely, we prove that the largest real scattering pole of a conformally compact Einstein manifold $(X,g)$ is less than $\ndemi -1$ if and only …

A new definition of umbilic points at infinity for polynomial surfaces.

The paper characterizes ambient metrics using conformal completion and null infinity properties.

The study shows that certain conformal classes on S^7 cannot be conformal infinities of Poincaré-Einstein metrics.

The paper explores conformal groups on plane waves and proves a conjecture in locally homogeneous settings.

The paper solves fractional scalar curvature problems on conformal infinities.

Classifies 1-connected Lorentzian manifolds with essential conformal groups.

In the complex-Riemannian framework we show that a conformal manifold containing a compact, simply-connected, null-geodesic is conformally flat. In dimension 3 we use the LeBrun correspondence, that views a conformal 3-manifold as the conformal infinity of a selfdual four-manifolds. We also find a relation between the …

Constructed static vacuum metrics in 5D with negative cosmological constant.

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null…

Study Cheeger constant and Yamabe type for ALH manifolds.

We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat homogeneous Ricci solitons.

The paper analyzes null infinity's geometry without restrictions.

In this paper we prove that under a lower bound on the Ricci curvature and an asymptotic assumption on the scalar curvature, a complete conformally compact manifold $(M^{n+1},g)$, with a pole $p$ and with the conformal infinity in the conformal class of the round sphere, has to be the hyperbolic space.

Study proves conformal vector fields on certain Finsler manifolds are Killing fields.

We derive a relationship between the eigenvalues of the Weyl-Schouten tensor of a conformal representative of the conformal infinity of a hyperbolic Poincaré manifold and the principal curvatures on the level sets of its uniquely associated defining function with calculations based on [9] [10]. This relationship genera…

Study the fractional Yamabe problem on locally flat conformal infinities of Poincaré-Einstein manifolds.

Study asymptotics of Poisson kernel and Green's functions for fractional conformal Laplacian.

This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is of positive scalar curvature. We find in particular that general solvability in …

We classify non-reductive four-dimensional homogeneous conformally Einstein manifolds.

Study characterizes conformal boundaries of de Sitter spacetimes.

Paper proves rigidity of Poincaré-Einstein manifolds with cylindrical conformal infinities.

Researchers use conformal infinity to study spacetimes near AdS2×S2.

We prove various classification results for homogeneous locally conformally symplectic manifolds. In particular, we show that a homogeneous locally conformally Kaehler manifold of a reductive group is of Vaisman type, if the normalizer of the isotropy group is compact. We also show that such a result does not hold in t…

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that t…

The conformal infinity of a quaternionic-Kahler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n-1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kahler metric. On the contrary, in dim…

We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with boundary at infinity a conformal metric, we prove that if the obstruction vanishes, on…

In this paper we first use the result in $[12]$ to remove the assumption of the $L^2$ boundedness of Weyl curvature in the gap theorem in $[9]$ and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey of known results along with some new results and observations; in particular we…

Generalizing Riemannian theorems of Anderson-Herzlich and Biquard, we show that two $(n+1)$-dimensional stationary vacuum space-times (possibly with cosmological constant $Λ\in \R$) that coincide up to order one along a timelike hypersurface $\mycal T$ are isometric in a neighbourhood of $\mycal T$. We further prove th…

Study of Lorentzian manifolds with specific transformations.

New tensors capture intrinsic embedding data of conformal hypersurfaces.

In this paper we study the invariant Walker structures over the conformally flat four-dimensional homogeneous manifolds according to the Seger types of the Ricci operator.

The hyperbolic space is the only conformally compact Poincaré-Einstein manifold with a round sphere boundary.

We present a novel approach to the classification of conformally equivariant differential operators on spinors in the case of homogeneous conformal geometry. It is based on the classification of solutions for a vector-valued system of partial differential equations, associated to $\mathcal{D}$-modules for the homogeneo…

Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.

New types of Einstein manifolds discovered from homogeneous surfaces.

Study on unique solutions to one-phase free boundary problems.

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional on such conformal classes, near homogeneous metrics. Both bifurcation and local…