Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

ELLIPSOMETER/POLARMETERBASED PROCESS MONITOR AND CONTROL SYSTEM SUITABLE FOR SIMULTANEOUS RETROFIT ON MOLECULAR BEAM EPITAXY SYSTEM RHEED/LEED INTERFACE SYSTEM, AND METHOD OF USE

A method of, and system for applying light beam producing systems, such as ellipsometers, polarimeters, polarized light reflectance and functionally similar systems, such that a beam of light produced thereby is caused to be incident upon a process element at an angle in excess of an associated Brewster angle while enabling the production of a signal sufficiently sensitive to changes in process element parameters, for use in real-time process element process monitoring and control, is disclosed. In addition, a process element processing system and electron beam producing system and light beam producing system combination system is taught, wherein the electron beam producing and light beam producing systems are mounted to the process element processing system (typically a (MBE) system), by input and output interface system present at a location appropriate for conventional Reflection High Energy Electron Diffraction (RHEED) systems

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

Rigid spheres in Riemannian spaces

Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of the Cauchy space, leads often to a substantial simplification of various mathematical problems in General Relativity Theory. We propose a new method to construct such foliations. For this purpose we define a special family of topological two-spheres, which we call "rigid spheres". We prove that there is a four-parameter family of rigid spheres in a generic Riemannian three-manifold (in case of the flat Euclidean three-space these four parameters are: 3 coordinates of the center and the radius of the sphere). The rigid spheres can be used as building blocks for various ("spherical", "bispherical" etc.) foliations of the Cauchy space. This way a supertranslation ambiguity may be avoided. Generalization to the full 4D case is discussed. Our results generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page

Ricci flows with bursts of unbounded curvature

Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metric, this Ricci flow always exists for all time and converges (after scaling by a factor 1/2t ) to this hyperbolic metric [GT11], i.e. our Ricci flow geometrises the surface. In this paper we show that there exist complete, bounded curvature initial metrics, including those conformal to a hyperbolic metric, which have subsequent Ricci flows developing unbounded curvature at certain intermediate times. In particular, when coupled with the uniqueness from [Top13], we find that any complete Ricci flow starting with such initial metrics must develop unbounded curvature over some intermediate time interval, but that nevertheless, the curvature must later become bounded and the flow must achieve geometrisation as t → ∞, even though there are other conformal deformations to hyperbolic metrics that do not involve unbounded curvature. Another consequence of our constructions is that while our Ricci flow from [GT11] must agree initially with the classical flow of Hamilton and Shi in the special case that the initial surface is complete and of bounded curvature, by uniqueness, it is now clear that our flow lasts for a longer time interval in general, with Shi’s flow stopping when the curvature blows up, but our flow continuing strictly beyond in these situations. All our constructions of unbounded curvature developing and then disappearing are in two dimensions. Generalisations to higher dimensions are then immediate

The coronary CT angiography vision protocol : a prospective observational imaging cohort study in patients undergoing non-cardiac surgery

INTRODUCTION: At present, physicians have a limited ability to predict major cardiovascular complications after non-cardiac surgery and little is known about the anatomy of coronary arteries associated with perioperative myocardial infarction. We have initiated the Coronary CT Angiography (CTA) VISION Study to (1) establish the predictive value of coronary CTA for perioperative myocardial infarction and death and (2) describe the coronary anatomy of patients that have a perioperative myocardial infarction. METHODS AND ANALYSIS: The Coronary CTA VISION Study is prospective observational study. Preoperative coronary CTA will be performed in 1000–1500 patients with a history of vascular disease or at least three cardiovascular risk factors who are undergoing major elective non-cardiac surgery. Serial troponin will be measured 6–12 h after surgery and daily for the first 3 days after surgery. Major vascular outcomes at 30 days and 1 year after surgery will be independently adjudicated. ETHICS AND DISSEMINATION: Coronary CTA results in a measurable radiation exposure that is similar to a nuclear perfusion scan (10–12 mSV). Treating physicians will be blinded to the CTA results until 30 days after surgery in order to provide the most unbiased assessment of its prognostic capabilities. The only exception will be the presence of a left main stenosis >50%. This approach is supported by best available current evidence that, excluding left main disease, prophylatic revascularisation prior to non-cardiac surgery does not improve outcomes. An external safety and monitoring committee is overseeing the study and will review outcome data at regular intervals. Publications describing the results of the study will be submitted to major peer-reviewed journals and presented at international medical conferences