Curvature estimates for submanifolds in warped products

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.Comment: 21 page

The mean curvature of cylindrically bounded submanifolds

We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabion complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title (February 2009). To appear in Mathematische Annale

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $\Omega \subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Late

Foxm1 modulates cell non-autonomous response in zebrafish skeletal muscle homeostasis

Foxm1 is a master regulator of the cell cycle, contributing to cell proliferation. Recent data have shown that this transcription factor also modulates gene networks associated with other cellular mechanisms, suggesting non-proliferative functions that remain largely unexplored. In this study, we used CRISPR/Cas9 to disrupt foxm1 in the zebrafish terminally differentiated fast-twitching muscle cells. foxm1 genomic disruption increased myofiber death and clearance. Interestingly, this contributed to non-autonomous satellite cell activation and proliferation. Moreover, we observed that Cas9 expression alone was strongly deleterious to muscle cells. Our report shows that foxm1 modulates a muscle non-autonomous response to myofiber death and highlights underreported toxicity to high expression of Cas9 in vivo.This study was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-2015-StG-680156-ZPR). FEDER (Fundo Europeu de Desenvolvimento Regional) funds through the COMPETE 2020—Operational Programme for Competitiveness and Internationalization (POCI), Portugal 2020 and by Portuguese funds through FCT (Fundação para a Ciência e a Tecnologia) in the framework of the project POCI-01-0145-FEDER-031120 (PTDC/BIA-CEL/31120/2017); and POCI-01-0145-FEDER-007274 i3S framework project co-funded by COMPETE 2020/PORTUGAL 2020 through FEDER. E.L. and J.B. are supported by FCT (J.B.: Grant CEECIND/03482/2018; E.L.: Grants CEECIND/00654/2020 and IF/00916/2014). F.J.F. (PD/BD/105745/2014) is a PhD fellow from FCT

Impact of COVID-19 on maternal health and child care behavior: evidence from a quasi-experimental study of vulnerable communities in Boa Vista, Brazil

BACKGROUND: COVID-19 related distress has been shown to have negative associations with family well-being. OBJECTIVES: To determine the immediate impact of acute COVID-19 infection on maternal well-being and parenting practices among Brazilian families. PARTICIPANTS AND SETTING: We studied 2'579 mothers (29'913 observations) of young children from vulnerable neighborhoods in Boa Vista, Brazil over 12 months. METHODS: We monitored family health and caregiving behavior including the incidence of COVID-19 infections in the surveyed households through bi-weekly phone interviews over 50 weeks, from June 2020 to May 2021. Primary outcomes were home-based child stimulation, positive parenting behavior, and parenting stress. We used fixed effects panel regressions to estimate the impact of household COVID-19 infections on parenting outcomes. RESULTS: Over the study period, 441 participants (17.1%; 831 (3.0%) observations) reported at least 1 positive COVID-19 infection in their household. Household COVID-19 infections significantly reduced home-based stimulation by 0.10 SDs (95%CI: -0.18, -0.01), positive parenting behaviors by 0.14 SDs (-0.21, -0.01), and increased parenting stress by 0.07 SDs (0.02, 0.12). The impact on home-based stimulation was most pronounced when the mother herself had a COVID-19 infection (-0.16; -0.29, -0.04). Parenting stress responded most strongly to mother or child COVID-19 infections. Effects were relatively short-lived, only children's infections' on parental stress was still detectable 2 weeks after initial infection. CONCLUSION: Our findings suggest that COVID-19 infections cause substantial disruptions in children's home environments - additional short-term support for families with acute infections could attenuate the negative impact on children's home environment during the pandemic