Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M , and that the double cosets for crossing surfaces are also separable. We deduce that if there is a ‘sufficient’ collection of surfaces in M , then π1M is virtually the fundamental group of a special non-positively curved cube complex. We provide a sufficient collection for ...

We prove that a smooth compact immersed submanifold of codimension 2 in R, n ≥ 3, bounds at most finitely many topologically distinct compact nonnegatively curved hypersurfaces. Analogous results for complete fillings of arbitrary Riemannian submanifolds are obtained as well. On the other hand, we show that these finiteness theorems may not hold if the codimenion is too high, or the prescribed ...

We start from a given Lorentz metric and a vector field of world lines along which observers and measure devices may move. We describe a procedure to associate one-particle Hilbert spaces and one-particle Hamiltonians to space-like hypersurfaces using a transi, tion to a Riemannian metric. With the aid of suitable boundary conditions one can confine the particle within a world tube ("box quanti...

We consider the h-p Galerkin boundary element method applied to a weakly singular integral equation of the rst kind on an open curved surface. We focus on the eeective computation of the Galerkin matrix, i.e. we introduce a numerical qudrature rule which is shown (for a model case) to converge exponentially fast with the number of kernel evaluations. Numerical experiments show that the applicat...

Gauged WZNWmodels are integrable conformal field theories. We integrate the classical SL(2,R)/U(1) theory with periodic boundary conditions, which describes closed strings moving in a curved targetspace geometry. We calculate its Poisson bracket structure by solving an initial state problem. The results differ from previous fieldtheoretic calculations due to zero modes. For a future exact canon...

We propose a new technique to implement solid wall boundary conditions for steady two-dimensional Euler equations for problems in curved geometries. The technique is to be used with high-order methods on unstructured, straight-sided element meshes. By modeling flow around a physical rather than computational geometry, significant improvement in quality of the solution is achieved. The technique...

The quasi-static evolution of an elastoplastic body with a multi-surface constitutive law of linear kinematic hardening type allows the modeling of curved stress-strain relations. It generalizes classical small-strain elastoplasticity from one to various plastic phases. This paper presents the mathematical models and proves existence and uniqueness of the solution of the corresponding initial-b...

We consider the problem of searching a polygonal room with two guards starting at a specified door point. While maintaining mutual visibility and without crossing the door, the guards must move along the boundary of the room and eventually meet again. We give polynomial time algorithms for finding a search schedule that minimizes the total distance travelled by the guards and for minimizing the...