Extending invariant complex structures

We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either h is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of g. Constructive examples illustrating this situation are shown, in particular computations in dimension six are given.Comment: 22 pages, plus an Addendu

Job flow dynamics and firing restrictions: evidence from Europe

We exploit homogeneous firm level data of manufacturing and non-manufacturing sectors to study the impact of firing restrictions on job flow dynamics across 14 European countries. We find that more stringent firing laws dampen the response of job destruction to the cycle, thus making job turnover less counter-cyclical. Moreover, the impact of firing costs on job creation and job destruction varies across sectors, depending on sector-specific trend growth. Our findings clearly suggest that such costs are more important in contracting than in growing sectors. JEL Classification: J23, J63, J68business cycle, Europe, Firing Costs, Gross Job Flows

The cyclical behavior of equilibrium unemployment and vacancies revisited

Recently, a number of authors have argued that the standard search model cannot generate the observed business-cycle-frequency fluctuations in unemployment and job vacancies, given shocks of a plausible magnitude. We use data on the cost of vacancy creation and cyclicality of wages to identify the two key parameters of the model - the value of non-market activity and the bargaining weights. Our calibration implies that the model is, in fact, consistent with the data. JEL Classification: E24, E32, J41, J63, J64business cycles, labor markets, Matching, Search

Global Well-posedness for 2D Nonlinear Wave Equations without Compact Support

In the significant work of [2], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [22]. Whether this constraint can be removed or not is still unclear. In this paper, for fully nonlinear wave equations under the null conditions, we prove the global well-posedness for small initial data without compact support. Moreover, we apply our result to a class of quasilinear wave equations.Comment: To appear in J. Math. Pures App