Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position.Comment: 42 pages, 8 figures. v2: typos correcte

Nematic Films and Radially Anisotropic Delaunay Surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure

On "many black hole" space-times

We analyze the horizon structure of families of space times obtained by evolving initial data sets containing apparent horizons with several connected components. We show that under certain smallness conditions the outermost apparent horizons will also have several connected components. We further show that, again under a smallness condition, the maximal globally hyperbolic development of the many black hole initial data constructed by Chrusciel and Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an event horizon, the intersection of which with the initial data hypersurface is not connected. This justifies the "many black hole" character of those space-times.Comment: several graphic file

Upper bounds for the eigenvalues of Hessian equations

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur

Bronchoalveolar Activation of Coagulation and Inhibition of Fibrinolysis during Ventilator-Associated Lung Injury

Background and Objective. Bronchoalveolar coagulopathy is a characteristic feature of pulmonary inflammation. We compared bronchoalveolar and systemic levels of coagulation in patients who did and patients who did not develop ventilator-associated lung injury (VALI). Methods. Secondary analysis of a randomized controlled trial evaluating the effect of lower tidal volumes versus conventional tidal volumes in patients without acute lung injury or acute respiratory distress syndrome at the onset of mechanical ventilation. Results. Ten patients with VALI and 10 random control patients without lung injury during the course of mechanical ventilation, but all ventilated with conventional tidal volumes, were compared. Patients who developed VALI showed both bronchoalveolar activation of coagulation (increase in thrombin–antithrombin complex levels P < 0.001 versus baseline) and inhibition of fibrinolysis (decline in plasminogen activator activity P < 0.001 versus baseline). The later seemed to be dependent on higher levels of plasminogen activator inhibitor type 1 (P = 0.001 versus baseline). Patients who developed VALI also showed elevated systemic thrombin-antithrombin complex levels and decreased systemic plasminogen activator activity levels. Conclusions. VALI is characterized by bronchoalveolar coagulopathy. Systemic and bronchoalveolar coagulopathy at the onset of mechanical ventilation may be a risk factor for developing VALI in patients ventilated with conventional tidal volumes

Interference by new-generation mobile phones on critical care medical equipment

GPRS, UMTS en medische apparatuur in het ziekenhui

Closed geodesics in Alexandrov spaces of curvature bounded from above

In this paper, we show a local energy convexity of $W^{1,2}$ maps into $CAT(K)$ spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout construction to produce closed geodesics in any closed Alexandrov space of curvature bounded from above, which also provides a generalized version of the Birkhoff-Lyusternik theorem on the existence of non-trivial closed geodesics in the Alexandrov setting.Comment: Final version, 22 pages, 2 figures, to appear in the Journal of Geometric Analysi

Distributional versions of Littlewood's Tauberian theorem

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Ces\`{a}ro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.Comment: 15 page

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series