A bstract Celestial diamonds encode the global conformal multiplets of conformally soft sector, elucidating role theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat charges associated to fermionic layers that tie this structure together. This extends analysis currents for photons gravitons which have been shown generate asymptoti...

A well-known open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe's paper claimed to solve the problem in the affirmative, it was found by N. Trudinger [6] in 1968 tha...

We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.

OBJECTIVE Early recurrency after surgery for acute endocarditis is a life-threatening complication. Allograft valves are supposed to have a higher resistance to recurrent infection, thus several authors claim them to be the replacement device of choice in cases of aortic endocarditis. However, allografts have two major drawbacks: their availability is limited, and most of the patients require r...

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class of groups, amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk’s group, Basilica group, groups associated with...

The energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved surface moving by uniform proper accelerations in static de Sitter spacetime is investigated. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expect...

We analyze the relationship between quasilocal masses calculated for solutions of conformally related theories. We show that the adm mass of a static, spherically symmetric solution is conformally invariant (up to a constant factor) only if the background action functional is conformally invariant. Thus, the requirement of conformal invariance places restrictions on the choice of reference spac...