Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

A Note on Real Tunneling Geometries

In the Hartle-Hawking ``no boundary'' approach to quantum cosmology, a real tunneling geometry is a configuration that represents a transition from a compact Riemannian spacetime to a Lorentzian universe. I complete an earlier proof that in three spacetime dimensions, such a transition is ``probable,'' in the sense that the required Riemannian geometry yields a genuine maximum of the semiclassical wave function.Comment: 5 page

Ricci flows, wormholes and critical phenomena

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that observed in gravitational collapse. Similar results are obtained for initial data that describe space bubbles attached to asymptotically flat regions. Our numerical methods are applicable to "matter-coupled" Ricci flows derived from conformal invariance in string theory.Comment: 8 pages, 5 figures. References added and minor changes to match version accepted by CQG as a fast track communicatio

is it worse when raising children alone?

© The Author(s) 2021. Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved. For permissions, please e-mail: [email protected]: Paid employment has been shown to benefit childless women's health, while employed mothers experience poorer health, and more pronounced fatigue. This study measures the association between job characteristics and the health and well-being of employed mothers and the differential susceptibility to job characteristics between coupled and single-parent mothers. METHODS: We used data from the 5th Portuguese National Health Survey from 1649 employed women (aged 25-54) living with a child under 16. We modelled depression (assessed by the Personal Health Questionnaire-8) and self-reported health as a function of job characteristics, adding interaction terms to compare coupled and single-parent mothers, using logistic regressions. RESULTS: Working part-time was associated with depression (odds ratio (OR) = 3.39, 95% confidence interval (CI) = 3.31-3.48) and less-than-good health (OR = 1.28, 95%CI = 1.26-1.31), compared to working full time. Compared to high-skill jobs, the likelihood for depression among low-skill occupations was lower among coupled mothers (OR = 0.25, 95%CI = 0.24-0.26), and higher among single-parent mothers (OR = 1.75, 95%CI = 1.54-1.99). Unstable jobs were associated with depression among coupled mothers. CONCLUSIONS: Part-time jobs are detrimental for mothers' mental health, but high-skilled jobs are protective for single-parent mothers. Part-time and unstable jobs are linked to poorer self-reported health among coupled mothers. Results question the gendered arrangements that may face employed coupled mothers.publishersversionepub_ahead_of_prin

The Simplicial Ricci Tensor

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension.Comment: 19 pages, 2 figure

The layered crisis of the primary care medical workforce in the European region: what evidence do we need to identify causes and solutions?

Publisher Copyright: © 2023, The Author(s).Primary care services are key to population health and for the efficient and equitable organisation of national health systems. This is why they are often financed through public funds. Primary care doctors are instrumental for the delivery of preventive services, continuity of care, and for the referral of patients through the system. These cadres are also the single largest health expenditure at the core of such services. Although recruitment and retention of primary care doctors have always been challenging, shortages are now exacerbated by higher demand for services from aging populations, increased burden of chronic diseases, backlogs from the COVID-19 pandemic, and patient expectations. At the same time, the supply of primary care physicians is constrained by rising retirement rates, internal and external migration, worsening working conditions, budget cuts, and increased burnout. Misalignment between national education sectors and labour markets is becoming apparent, compounding staff shortages and maldistribution. With their predominantly publicly funded health systems and in the aftermath of COVID-19, countries of the European region appear to be now on the cusp of a multi-layered, slow-burning primary care crisis, with almost every country reporting long waiting lists for doctor appointments, shortages of physicians, unfilled vacancies, and consequently, added pressures on hospitals’ Accident and Emergency services. This articles collection aims at pulling together the evidence from countries of the European Region on root causes of such workforce crisis, impacts, and effectiveness of existing policies to mitigate it. Original research is needed, offering analysis and fresh insights into the primary care medical workforce crisis in wider Europe. Ultimately, the aim of this articles collection is to provide an evidence basis for the identification of policy solutions to present and future primary health care crises in high as well as lower-income countries.publishersversionpublishe

Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the canonical ensemble for gravity in a box. At high temperature the action has three saddle points: hot flat space and a large and small black hole. Adding a time direction, these also give static 5-dimensional Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action. The small black hole has a Gross-Perry-Yaffe-type negative mode, and is therefore unstable under Ricci flow. We numerically simulate the two flows seeded by this mode, finding that they lead to the large black hole and to hot flat space respectively, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space of metrics corrected and expanded, references adde

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit