A novel type of Sobolev-Poincar\'e inequality for submanifolds of Euclidean space

For functions on generalised connected surfaces (of any dimensions) with boundary and mean curvature, we establish an oscillation estimate in which the mean curvature enters in a novel way. As application we prove an a priori estimate of the geodesic diameter of compact connected smooth immersions in terms of their boundary data and mean curvature. These results are developed in the framework of varifolds. For this purpose, we establish that the notion of indecomposability is the appropriate substitute for connectedness and that it has a strong regularising effect; we thus obtain a new natural class of varifolds to study. Finally, our development leads to a variety of questions that are of substance both in the smooth and the nonsmooth setting.Comment: 35 pages, no figure

An isoperimetric inequality for diffused surfaces

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.Comment: Awaiting publication in Kodai Math. J. The final printed version will be different. 14 pages, no figure

The effects of financing rules in pay-as-you-go pension systems on the life and the business cycle

I study the impacts of financing rules for financial surpluses in pay-as-you-go pension systems on the business cycle and the life cycle in a dynamic stochastic large-scale overlapping generations model, where households take the inter-temporal links between contributions and pension benefits explicitly into account. The results point out that sluggish adjustments of contribution rates that are implemented by adjusting a financial buffer stock both stabilize an economy and decrease the volatility of life-time utilities of retirees and workers close to retirement. Such a policy allows these households a better hedge against macroeconomic shocks over the business cycle. Moreover, I show that the impacts of higher fluctuations of aggregate variables on the volatility of individual lifetime utilities can rather be negligible

Properties of surfaces with spontaneous curvature

A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower semi-continuous with respect to oriented varifold convergence on a space of surfaces whose second fundamental form is uniformly bounded in $L^2$. Elementary examples are presented showing that the latter condition is necessary. As a consequence, smoothly embedded minimisers among surfaces of higher genus are obtained. Moreover, it is shown that the diameter of a connected surface is controlled by the $L^1$-deficit of its mean curvature to the spontaneous curvature leading to an improved condition for the existence of minimisers. Finally, the diameter bound can be applied to obtain an isoperimetric inequality.Comment: 37 pages, no figure

Embedded Delaunay tori and their Willmore energy

A family of embedded rotationally symmetric tori in the Euclidean 3-space consisting of two opposite signed constant mean curvature surfaces that converge as varifolds to a double round sphere is constructed. Using complete elliptic integrals, it is shown that their Willmore energy lies strictly below $8\pi$. Combining such a strict inequality with previous works by Keller-Mondino-Rivi\`ere and Mondino-Scharrer allows to conclude that for every isoperimetric ratio there exists a smoothly embedded torus minimising the Willmore functional under isoperimetric constraint, thus completing the solution of the isoperimetric-constrained Willmore problem for tori. Similarly, we deduce the existence of smoothly embedded tori minimising the Helfrich functional with small spontaneous curvature. Moreover, it is shown that the tori degenerate in the moduli space which gives an application also to the conformally-constrained Willmore problem. Finally, because of their symmetry, the Delaunay tori can be used to construct spheres of high isoperimetric ratio, leading to an alternative proof of the known result for the genus zero case.Comment: 28 pages. Final version to appear in Nonlinear Analysis (TMA

The Burden of Unanticipated Fiscal Policy

We study the impact of a government spending shock on the distribution of wealth and income between cohorts in a dynamic stochastic overlapping generations model with two types of households, a Ricardian household and a rule-of-thumb consumer. We demonstrate that an unexpected increase in government spending increases income inequality and decreases wealth inequality. In contrast to conventional wisdom that the financing of the additional expenditures by debt rather than taxes especially burdens young on behalf of the old generations, we find that a bond-financed increase in government spending rather harms the Ricardian households during both working age and retirement, while the rule-of-thumb consumers benefit at working age. The crucial element in our analysis is a wealth effect that results from the decline in the price of capital due to higher government debt

The Burden of Unanticipated Government Spending

We study the impact of a government spending shock on the distribution of income and wealth between cohorts in a dynamic stochastic Overlapping Generations model with two types of households, Ricardian households and rule-of-thumb consumers. We demonstrate that an unexpected increase in government spending increases income inequality and decreases wealth inequality. In contrast to the conventional wisdom that the financing of additional expenditures by debt rather than taxes especially burdens young generations, we find that a debt-financed increase in government spending also harms Ricardian households during retirement, while workers close to retirement benefit. The crucial element in our analysis is a wealth effect that results from the decline in the price of capital due to higher government debt

A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint

Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperimetric constraints. Building on previous work by Keller-Mondino-Rivi\`ere, our strict inequality leads to existence of minimisers for the isoperimetric constrained Willmore problem in every genus, provided the minimal energy lies strictly below $8\pi$. Besides the geometric interest, such a minimisation problem has been studied in the literature as a simplified model in the theory of lipid bilayer cell membranes.Comment: 16 pages. Final version to appear in Advances in Calculus of Variation

The fiscal and intergenerational burdens of brakes and subsidies for energy prices

We study the effects of different financing rules for untargeted energy price brakes and subsidies on intergenerational welfare in a large-scale overlapping generations model. The results indicate that, in comparison with a laissez-faire solution without any government interventions, debt-financed implementations of such measures are very detrimental for young and future generations. However, the taxation of windfall profits can significantly contribute to reduce the economic burdens of these generations; whereas, the positive effects on older generations are much less pronounced