We are interested in examples of compact, complete, locally CAT(-1) spaces X, and closed totally geodesic codimension two subspaces Y , with the property that ∂∞X̃ = Sn+2 ∞ , and ∂ ∞Ỹ = Sn ∞. We show that if the inclusion S n ∞ ↪→ Sn+2 ∞ induced by the inclusion Y ⊂ X is knotted, then it is a totally wild knot (i.e. nowhere tame). We give examples where the inclusion Sn ∞ ↪→ Sn+2 ∞ is indeed kno...

We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline pattern of dimples self-organizes on the surface of the shell. Stresses are relaxed by both out-of...

This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain Ω. Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain Ωh 6⊂ Ω in the framework of the abstract spectral approximation theory.

The finite elements considered in this paper are those of the Serendipity family of curved isoparametric elements. There is given a detailed analysis of a superconvergence phenomenon for the gradient of approximate solutions to second order elliptic boundary value problems. An approach is proposed how to use the superconvergence in practical computations.

We study the topology of a complete asymptotically hyperbolic Einstein manifold such that its conformal boundary has positive Yamabe invariant. We proved that all maps from such manifold into any nonpositively curved manifold are homotopically trivial. Our proof is based on a Bochner type argument on harmonic maps.

We prove the theorem: The necessary and suucient condition for a spherically symmetric spacetime to represent an isothermal perfect uid (barotropic equation of state with density falling oo as inverse square of the curvature radius) distribution without boundary is that it is conformal to the \minimally" curved (gravitation only manifesting in tidal acceleration and being absent in particle tra...

Powell–Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and N...

We propose a coarse-to-fine approach for generating fine and curved highorder tetrahedral meshes. The proposed approach is performed in three steps: (1) generate a coarse reference mesh; (2) map this to a coarse and curved highorder mesh; and (3) refine the curved high-order mesh. The approach provides high-order meshes that are valid, have the desired interpolation degree, and can be computed ...

We consider the propagation of sine-Gordon kinks in a planar curved strip as a model of nonlinear wave propagation in curved wave guides. The homogeneous Neumann transverse boundary conditions, in the curvilinear coordinates, allow to assume a homogeneous kink solution. Using a simple collective variable approach based on the kink coordinate, we show that curved regions act as potential barrier...