In this paper, we study the dilation limit of solutions to the Ricci flow on manifolds with nonnegative curvature operator. We first show that such a dilation limit must be a product of a compact ancient Type I solution of the Ricci flow with flat factors. Then we show under the Type I normalized Ricci flow, the compact factor has a subsequence converge to a Ricci soliton.

I will review some of the developments in studies of the host galaxy properties of Compact Steep Spectrum (CSS) and GigaHertz-Peaked Spectrum (GPS) radio sources. In contrast to previous reviews structured around observational technique, I will discuss the host galaxy properties in terms of morphology, stellar content and warm gas properties and discuss how compact, young radio-loud AGN are key...

Let (M, I) be a compact Kähler manifold admitting a hypercomplex structure (M, I, J,K). We show that (M, I, J,K) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M, I).

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

Let (M, I, J,K) be a compact hypercomplex manifold admitting a special kind of quaternionic-Hermitian metric called an HKT-metric. Assume that the canonical bundle of (M, I) is trivial as a holomorphic line bundle. We show that the holonomy of canonical torsion-free connection called Obata connection onM is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds which...

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...