Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities

We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the 2D case. On one hand we construct examples of nonuniqueness by showing that surfaces with cusps can evolve either by keeping the cusps or by contracting them. On the other hand, by adding a noncollapsedness assumption for the initial metric, we establish a uniqueness result

Global regularity of three-dimensional Ricci limit spaces

In their recent work [ST17], Miles Simon and the second author established a local bi-Hölder correspondence between weakly noncollapsed Ricci limit spaces in three dimensions and smooth manifolds. In particular, any open ball of finite radius in such a limit space must be bi-Hölder homeomorphic to some open subset of a complete smooth Riemannian three-manifold. In this work we build on the technology from [ST16, ST17] to improve this local correspondence to a global-local correspondence. That is, we construct a smooth three-manifold M, and prove that the entire (weakly) noncollapsed three-dimensional Ricci limit space is homeomorphic to M via a globally-defined homeomorphism that is bi-Hölder once restricted to any compact subset. Here the bi-Hölder regularity is with respect to the distance dg on M, where g is any smooth complete metric on M. A key step in our proof is the construction of local pyramid Ricci flows, existing on uniform regions of spacetime, that are inspired by Hochard’s partial Ricci flows [Hoc16]. Suppose (M, g0, x0) is a complete smooth pointed Riemannian three-manifold that is (weakly) noncollapsed and satisfies a lower Ricci bound. Then, given any k ∈ N, we construct a smooth Ricci flow g(t) living on a subset of spacetime that contains, for each j ∈ {1, . . . , k}, a cylinder Bg0 (x0, j) × [0, Tj ], where Tj is dependent only on the Ricci lower bound, the (weakly) noncollapsed volume lower bound and the radius j (in particular independent of k) and with the property that g(0) = g0 throughout Bg0 (x0, k).</p

Evaluating Mobile Device Cleaning Policies in the NHS

Introduction The use of mobile devices within healthcare settings by staff, patients and visitors is widespread and growing. DoH guidance states that patients should be allowed the widest possible use of mobile phones. For staff mobile devices have become an essential aspect of their day-to-day professional and personal lives. There is, however, clear evidence that phones/tablets can be contaminated with pathogens, which may survive for prolonged periods before being transferred onto hands or other surfaces.   Methods A FoI request for “all current policies or guidelines that make reference to the use and management of mobile phones and tablet devices in the healthcare environment, by staff, service users, and visitors – this applies to both personal and institutionally-owned devices”, was sent to NHS institutions across England, Scotland and Wales with a response rate of 96% (n=252).   Results 22% of organisations had no policy in place, with ≈11% stating that this would be considered policy reviews. Organisations that acknowledged the issue responded that staff were informed of disinfection procedures: e.g. ‘the normal cleaning schedule’ or the use of universal sanitizing/detergent wipes. Many organisations referred to their Cleaning and Decontamination policy, however none of these explicitly mentioned mobile devices. Instead, the general advice for electrical devices was to follow manufacturer’s instructions, as using any other process might invalidate warranties. Where specific cleaning policies were in place they advocated the use of ‘general purpose/universal detergent wipes’ without any technical justification. Multiple organisations suggested that existing hand decontamination procedures were sufficient to address this issue.   Discussion There is no consistency in infection control advice regarding the potential risks posed by the use of mobile devices. Regular cleaning may be a solution, but there is little evidence evaluating the available methods. The literature in this field calls for clear evidence-based guidelines for cleaning and disinfecting mobile devices