This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future, and which admit a foliation by constant mean curvature compact Cauchy surfaces.

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...

We consider QED in a constant axial vector background. Lorentz invariance violation(LIV) occurs through radiative corrections. A detailed study of the phenomenology of the model is carried out, clarifying important issues related to the various regularizations employed . In this context, the physical meaning of the cutoffs induced by LIV is emphasized. Finally, finite temperature radiative corr...

In this work, we use Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations to study some consequences of single photon emission, known as vacuum Cherenkov radiation, and photon decay processes in cosmic and gamma rays. These processes are forbidden in a Lorentz invariant theory but allowed under the hypothesis of LIV. We show that the emission ...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

A subsequence principle is obtained, characterizing Banach spacescontaining co' in the spirit of the author's 1974 characterization of Banachspaces containing II . Defiaition. A sequence(bj )in a Banach space is called strongly summing (s.s.)if (bj ) is a weak-Cauchy basic sequence so that whenever scalars (cj ) satisfysUPn II E~=I cijll < 00, thenECj converges.A...

A subsequence principle is obtained, characterizing Banach spacescontaining co' in the spirit of the author's 1974 characterization of Banachspaces containing II . Defiaition. A sequence(bj )in a Banach space is called strongly summing (s.s.)if (bj ) is a weak-Cauchy basic sequence so that whenever scalars (cj ) satisfysUPn II E~=I cijll < 00, thenECj converges.A...

Spacetimes with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry are shown to be timelike and null geodesically complete in the expanding direction, provided the data satisfy a certain size restriction.

We study the positivity preserving property for the Cauchy problem for the linear fourth order heat equation. Although the complete positivity preserving property fails, we show that it holds eventually on compact sets.