Willmore minimizers with prescribed isoperimetric ratio

Motivated by a simple model for elastic cell membranes, we minimize the Willmore functional among two-dimensional spheres embedded in R^3 with prescribed isoperimetric ratio

On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow

In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of revolution embedded in R^3 and satisfying periodic boundary conditions. We also give conditions for global existence of solutions and prove that solutions are real analytic in time and space. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability and bifurcation behavior, with the radius acting as a bifurcation parameter for the problem.Comment: 37 pages, 6 figures, To Appear in SIAM J. Math. Ana

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657

A classification theorem for Helfrich surfaces

In this paper we study the functional \SW_{\lambda_1,\lambda_2}, which is the the sum of the Willmore energy, $\lambda_1$-weighted surface area, and $\lambda_2$-weighted volume, for surfaces immersed in $\R^3$. This coincides with the Helfrich functional with zero `spontaneous curvature'. Our main result is a complete classification of all smooth immersed critical points of the functional with $\lambda_1\ge0$ and small $L^2$ norm of tracefree curvature. In particular we prove the non-existence of critical points of the functional for which the surface area and enclosed volume are positively weighted.Comment: 21 page

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

Family violence, war, and natural disasters: A study of the effect of extreme stress on children's mental health in Sri Lanka

Catani C, Jacob N, Schauer E, Kohila M, Neuner F. Family violence, war, and natural disasters: a study of the effect of extreme stress on children's mental health in Sri Lanka. BMC Psychiatry. 2008;8(1): 33.BACKGROUND: The consequences of war violence and natural disasters on the mental health of children as well as on family dynamics remain poorly understood. Aim of the present investigation was to establish the prevalence and predictors of traumatic stress related to war, family violence and the recent Tsunami experience in children living in a region affected by a long-lasting violent conflict. In addition, the study looked at whether higher levels of war violence would be related to higher levels of violence within the family and whether this would result in higher rates of psychological problems in the affected children. METHODS: 296 Tamil school children in Sri Lanka's North-Eastern provinces were randomly selected for the survey. Diagnostic interviews were carried out by extensively trained local Master level counselors. PTSD symptoms were established by means of a validated Tamil version of the UCLA PTSD Index. Additionally, participants completed a detailed checklist of event types related to organized and family violence. RESULTS: 82.4% of the children had experienced at least one war-related event. 95.6% reported at least one aversive experience out of the family violence spectrum. The consequences are reflected in a 30.4% PTSD and a 19.6% Major Depression prevalence. Linear regression analyses showed that fathers' alcohol intake and previous exposure to war were significantly linked to the amount of maltreatment reported by the child. A clear dose-effect relationship between exposure to various stressful experiences and PTSD was found in the examined children. CONCLUSION: Data argue for a relationship between war violence and violent behavior inflicted on children in their families. Both of these factors, together with the experience of the recent Tsunami, resulted as significant predictors of PTSD in children, thus highlighting the detrimental effect that the experience of cumulative stress can have on children's mental health

Rabies-Specific Antibodies: Measuring Surrogates of Protection against a Fatal Disease

Antibodies play a central role in prophylaxis against many infectious agents. While neutralization is a primary function of antibodies, the Fc- and complement-dependent activities of these multifunctional proteins may also be critical in their ability to provide protection against most viruses. Protection against viral pathogens in vivo is complex, and while virus neutralization—the ability of antibody to inactivate virus infectivity, often measured in vitro—is important, it is often only a partial contributor in protection. The rapid fluorescent focus inhibition test (RFFIT) remains the “gold standard” assay to measure rabies virus–neutralizing antibodies. In addition to neutralization, the rabies-specific antigen-binding activity of antibodies may be measured through enzyme-linked immunosorbent assays (ELISAs), as well as other available methods. For any disease, in selecting the appropriate assay(s) to use to assess antibody titers, assay validation and how they are interpreted are important considerations—but for a fatal disease like rabies, they are of paramount importance. The innate limitations of a one-dimensional laboratory test for rabies antibody measurement, as well as the validation of the method of choice, must be carefully considered in the selection of an assay method and for the interpretation of results that might be construed as a surrogate of protection

Exendin-4 Improves Glycemic Control, Ameliorates Brain and Pancreatic Pathologies, and Extends Survival in a Mouse Model of Huntington's Disease

OBJECTIVE—The aim of this study was to find an effective treatment for the genetic form of diabetes that is present in some Huntington's disease patients and in Huntington's disease mouse models. Huntington's disease is a neurodegenerative disorder caused by a polyglutamine expansion within the huntingtin protein. Huntington's disease patients exhibit neuronal dysfunction/degeneration, chorea, and progressive weight loss. Additionally, they suffer from abnormalities in energy metabolism affecting both the brain and periphery. Similarly to Huntington's disease patients, mice expressing the mutated human huntingtin protein also exhibit neurodegenerative changes, motor dysfunction, perturbed energy metabolism, and elevated blood glucose levels