[en] We present some new notions of smoothness of geometrical boundaries. The relations between the classical notions of smoothness and ours are also investigated. Finally, the extension of locally Lipschitz continuous functions is studied in connection with geometrical properties of their demands of definition. (author). 17 refs, 2 figs

[en] For each 1 ≤ n ≤ 6 we present formulas for the number of n-nodal curves in an n-dimensional linear systems on a smooth, projective surface. The method yields in particular the numbers of rational curves in the system of hyperplane sections of a generic K3-surface imbedded in Pⁿ by a complete system of curves of genus n as well as the number 17,601,000 of rational (singular) plane quintic curves in a generic quintic threefold. (author). 23 refs

[en] D-branes in curved backgrounds can be treated with techniques of boundary conformal field theory. We discuss the influence of scalar condensates on such branes, i.e. perturbations of boundary conditions by marginal boundary operators. A general criterion is presented that guarantees a boundary perturbation to be truly marginal in all orders of perturbation theory. Our results on boundary deformations have several interesting applications which are sketched at the end of this note. (orig.)

[en] A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed

[en] Suppose a spacetime M is a quotient of a spacetime V by a discrete group of isometries. It is shown how causality conditions in the two spacetimes are related, and how one can learn about the future causal boundary on M by studying structures in V. The relations between the two are particularly simple (the boundary of the quotient is the quotient of the boundary) if both V and M have spacelike future boundaries and if it is known that the quotient of the future completion of V is past-distinguishing. (That last assumption is automatic in the case of M being multi-warped.)

[en] Recently we have shown that for 2 + 1-dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider an angular dependent throat geometry embedded in a 2 + 1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided by a hypocycloid. That is, two flat 2 + 1 dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one. (orig.)

[en] Automorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described in some detail, with emphasis on the resulting stratification of the space of scalar field theories in terms of the group theoretic data associated to the shift symmetry, as well as the automorphic data that specifies the potential. The class of theories based on Eisenstein series provides a natural generalization of the model of j-inflation considered previously.

[en] Motivated by the recent interest in dynamical properties of topologically non-trivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge-Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and gauge-independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties

[en] The postulated tensor field represented by the anti-symmetric part of the extended metric tensor, appearing in the Christoffel symbols, is investigated. Three possible forms of the coupling between the new field and spinor field describing neutrinos are discussed. The cosmological role of the new field and its possibility to form a closed or open universe are investigated numerically. The question of the quantization of the new field is briefly reviewed. Energy and momentum of the tensor field are calculated in the frame of classical field theory and exact solution is given in the stationary case. The strongly nonlinear interaction between the postulated tensor field and the spinor currents causes the localization of charge with characteristic size of 10^-33m and leads to strong self-interaction of neutral fields. This may have an important effect on the structure of elementary particles. (D.Gy.)

[en] The Hagedorn transition in noncommutative open string theory (NCOS) is relatively simple because gravity decouples. For NCOS theories in no more than five space--time dimensions, the Hagedorn transition is second order, and the high temperature phase involves long, nearly straight fundamental strings separating from the D-brane on which the NCOS theory is defined. Above five spacetime dimensions interaction effects become important below the Hagedorn temperature. Although this complicates studies of the transition, we believe that the high temperature phase again involves long strings liberated from the bound state