We discuss the renormalization group improved effective action and running surface couplings in curved spacetime with boundary. Using scalar selfinteracting theory as an example, we study the influence of boundary effects to effective equations of motion in spherical cap and the relevance of surface running couplings to quantum cosmology and symmetry breaking phenomenon. Running surface couplin...

We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat Möbius strip are determined by their lens data. We also see by example that the flat Möbius strip is not determined by it’s scattering data. We then consider the case of negatively curved cylinders with convex boundary and show th...

Braneworld effective action is constructed by two different methods based respectively on the Dirichlet and Neumann boundary value problems. The equivalence of these methods is shown due to nontrivial duality relations between special boundary operators of these two problems. Previously known braneworld action algorithms in two-brane Randall-Sundrum model are generalized to curved branes with d...

Third-order differential equations arise in a variety of different areas of applied mathematics and physics, such as the deflection of a curved beam having a constant or varying cross section, three-layer beam, electromagnetic waves, or gravity-driven flows 1 . Recently, thirdorder boundary value problems have been studied extensively in the literature see, e.g., 2– 13 , and their references . ...

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity,...

A graph is of parabolic or hyperbolic type if the simple random walk on the vertices is, respectively, recurrent or transient. A plane triangulation graph is CP-parabolic or CP-hyperbolic if the maximal circle packing determined by the graph packs, respectively, the complex plane C or the Poincar e disk D. We examine the implications that (Gromov) negative curvature carries for determining type...

The use of finite elements in smooth domains leads naturally to polyhedral or piecewise polynomial approximations of the boundary. Hence the approximation error consists of two parts: the geometric part and the finite element part. We propose to exploit this decomposition in the error analysis by introducing an auxiliary problem defined in a polygonal domain approximating the original smooth do...

To study a noncompact Riemannian manifold, it is often useful to …nd a compacti…cation or attach a boundary. For example, in hyperbolic geometry a lot of investigation is carried out on the sphere at in…nity. An eminent illustration is Mostow’s proof of his rigidity theorem for hyperbolic manifolds [Mo]. More generally, if f M is simply connected and nonpositively curved, one can compactify it ...

We prove that whenever G is negatively curved and ? = G ZZ n acts geometrically on two CAT(0)-spaces X and X 0 , their visual boundaries are ?-equivariantly homeomorphic, answering aarmatively a question of Gromov in this special case. However, we give a simple example that shows that the natural ?-equivariant quasi-isometry from X to X 0 does not continuously extend to a homeomorphism of visua...