This paper is written in the spirit of constructive mathematics in the sense of Errett Bishop [3]. For a general introduction to constructive algebra see [11]. An algebraist with no background in constructive mathematics should have no trouble understanding the arguments, but might not see what obstacles are being overcome or sidestepped. From a procedural point of view, the di erence is that w...

We prove a removal of singularities result for Bach-flat metrics in dimension 4 under the assumption of bounded L2-norm of curvature, bounded Sobolev constant and a volume growth bound. This result extends the removal of singularities result for special classes of Bach-flat metrics obtained by Tian and Viaclovsby. For the proof we emulate Cheeger and Tian and analyze the decay rates of solution...

We consider the simple extension of the Standard Model in which an additional right handed neutrino propagates along a flat extra dimension, while the Standard Model fields are confined on a 3-brane. The fifth dimension is S/Z2 orbifold compactified. In this scenario, the neutrino mass can be naturally suppressed. By studying systematically the fundamental parameter space, we show that the stro...

A method is presented to search for a hypertorus symmetry axis by the alignment of distant objects. This offers greater sensitivity than previously proposed object-based methods that rely on accurate true distances. When applied to the catalog of objects with z > 1, we find no evidence for a compact dimension. We deduce a lower limit to the compact dimension size D > 0.9 of the distance to the ...

We consider an asymptotically flat Lorentzian manifold of dimension (1, 3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.

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 ≥ 5 and with Poincarë exponent less than n−4 2 , the set of conformal metrics of positive constant Q and positive scalar curvature is compact in the C∞ topology.