Related papers: Spectral characterization of Poincar\'e-Einstein m…

Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…

Peng Wu recently announced a beautiful characterization of conformally Kaehler, Einstein metrics of positive scalar curvature on compact oriented 4-manifolds via the condition det (W^+) > 0. In this note, we buttress his claim by providing…

Let $X$ be an asymptotically hyperbolic manifold and $M$ its conformal infinity. This paper is devoted to deduce several existence results of the fractional Yamabe problem on $M$ under various geometric assumptions on $X$ and $M$: Firstly,…

In this work, we investigate the geometry and topology of compact Einstein-type manifolds with nonempty boundary. First, we prove a sharp boundary estimate, as consequence we obtain under certain hypotheses that the Hawking mass is bounded…

We study the renormalized volume of asymptotically hyperbolic Einstein (AHE in short) manifolds $(M,g)$ when the conformal boundary $\pl M$ has dimension $n$ even. Its definition depends on the choice of metric $h_0$ on $\partial M$ in the…

Let $(X,g)$ be a compact Riemannian manifold with quasi-positive Riemannian scalar curvature. If there exists a complex structure $J$ compatible with $g$, then the canonical bundle $K_X$ is not pseudo-effective and the Kodaira dimension…

In this note we study the conformal metrics of constant $Q$ curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension $n\geq 5$ and with Poincar\"{e} exponent less than…

Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface.…

We extend the following result of Cochran ``A closed $m$-quasi Einstein manifold ($M,g,X$) with $m \ne -2$ has constant scalar curvature if and only if $X$ is Killing" covering the missing accidental case $m=-2$ and generalize it showing…

Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n \ge 5$ and…

In this talk we introduce the properties of scattering forms on the compactified moduli space of Riemann spheres with $n$ marked points. These differential forms are $\text{PSL}(2,\mathbb{C})$ invariant, their intersection numbers…

We introduce a new functional $\mathcal{E}_{\mathfrak{p}}$ on the space of conformal structures on an oriented projective manifold $(M,\mathfrak{p})$. The nonnegative quantity $\mathcal{E}_{\mathfrak{p}}([g])$ measures how much…

Let Gamma be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent alpha. Let M_Gamma be the Gamma-quotient of the open unit ball. We consider certain…

Momentum space Ward identities are derived for the amputated n-point Green's functions in 3+1 dimensional non-relativistic conformal field theory. For n=4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green's…

A classical theorem in conformal geometry states that on a manifold with non-positive Yamabe invariant, a smooth metric achieving the invariant must be Einstein. In this work, we extend it to the singular case and show that in all…

The minimal volume of a closed manifold $M$ is the infimum of the volume of $(M,g)$ over all metrics $g$ with sectional curvature between $-1$ and $1$. We introduce a variant called the essential minimal volume, $\mathrm{ess-Minvol}(M)$,…

In this paper, we study some intrinsic characterization of conformally compact manifolds. We show that, if a complete Riemannian manifold admits an essential set and its curvature tends to -1 at infinity in certain rate, then it is…

Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also…

In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low energy…

Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and…