Schottky groups acting on homogeneous rational manifolds

We systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori's well-known construction. This yields new examples of non-K\"ahler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to L\'arusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of SL(2,C)/\Gamma for \Gamma a discrete free loxodromic subgroup of SL(2,C), previously obtained by A. Guillot.Comment: 30 pages; minor modifications, references have been added; to appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal

Regulation and competition in German banking: an assessment

In Germany a public discussion on the "power of banks" has been going on for decades now with power having at least two meanings. On the one hand it is the power of banks to control public corporations through direct shareholdings or the exercise of proxy votes - this is the power of banks in corporate control. On the other hand it is market power - due to imperfect competition in markets for financial services - that banks exercise vis-à-vis their loan and deposit customers. In the past, bank regulation has often been blamed to undermine competition and the working of market forces in the financial industry for the sake of soundness and stability of financial services firms. This chapter tries to shed some light on the historical development and current state of bank regulation in Germany. In so doing it tries to embed the analysis of bank regulation into a more general industrial organisation framework. For every regulated industry, competition and regulation are deeply interrelated as most regulatory institutions - even if they do not explicitly address the competitiveness of the market - either affect market structure or conduct. This paper tries to uncover some of the specific relationships between monetary policy, government interference and bank regulation on the one hand and bank market structure and economic performance on the other. In so doing we hope to point to several areas for fruitful research in the future. While our focus is on Germany, some of the questions that we raise and some of our insights might also be applicable to banking systems elsewhere. Revised version forthcoming in "The German Financial System", edited by Jan P. Krahnen and Reinhard H. Schmidt, Oxford University Press

The Economic Effects of Restrictions on Government Budget Deficits: Imperfect Privte Credit Markets

We consider a pure-exchange overlapping-generations model We consider a pure-exchange overlapping-generations model with many consumers per generation and many goods per period. As in Ghiglino and Shell (2000), there is a government that collects taxes, distributes transfers and faces budget deficit restrictions. We introduce, for realism and symmetry with the government, imperfection in the private credit markets. We find that with constraints on individual credit and anonymous (i.e., non-personalized) lump-sum taxes, strong (or 'global') irrelevance of the government budget deficit is not possible, and weak irrelevance can hold only in very special situations. With credit constraints and anonymous consumption taxes, weak irrelevance holds provided the number of tax instruments is sufficiently large and at least one consumer's credit constraint is not binding.

A convex analysis approach to optimal controls with switching structure for partial differential equations

Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality system that allows an explicit pointwise characterization and whose Moreau-Yosida regularization is amenable to a semismooth Newton method in function space. This approach is especially suited for computing switching controls for partial differential equations. In this case, the optimality gap between the original functional and its relaxation can be estimated and shown to be zero for controls with switching structure. Numerical examples illustrate the effectiveness of this approach

Homogeneous K\"ahler and Hamiltonian manifolds

We consider actions of reductive complex Lie groups $G=K^C$ on K\"ahler manifolds $X$ such that the $K$--action is Hamiltonian and prove then that the closures of the $G$--orbits are complex-analytic in $X$. This is used to characterize reductive homogeneous K\"ahler manifolds in terms of their isotropy subgroups. Moreover we show that such manifolds admit $K$--moment maps if and only if their isotropy groups are algebraic.Comment: 12 pages. The statement of Theorem 3.5 has been improve

Total variation regularization of multi-material topology optimization

This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming prespecified values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.