We consider systems of two wave/heat/Schrödinger-type equations coupled by a zero order term, only one of them being controlled. We prove an internal and a boundary null-controllability result in any space dimension, provided that both the coupling and the control regions satisfy the Geometric Control Condition. This includes several examples in which these two regions have an empty intersection.

Geometric rigidity states that a gradient field which is L-close to the set of proper rotations is necessarily L-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in L + L and in L interpolation spaces. As a fir...

We establish compactness estimates for ∂M on a compact pseudoconvex CRsubmanifold M of C of hypersurface type that satisfies the (analogue of the) geometric sufficient conditions for compactness of the ∂-Neumann operator given in [30, 22]. These conditions are formulated in terms of certain short time flows in complex tangential directions.

We present geometric conditions that can be used to restrict or eliminate candidate topologes for Euclidean Steiner minimal trees in , d ≥ 2. Our emphasis is on conditions that are not restricted to the planar case (d = 2). For trees with a Steiner topology we give restrictions on terminal-Steiner connections that are based on the Voronoi diagram associated with the set of terminal nodes. We th...

Curve subdivision is a technique for generating smooth curves from initial control polygons by repeated refinement. The most common subdivision schemes are based on linear refinement rules, which are applied separately to each coordinate of the control points, and the analysis of these schemes is well understood. Since the resulting limit curves are not sufficiently sensitive to the geometry of...

Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.

This paper aims to simplify the continuity conditions of Bézier curves. For this purpose, a special family of Bézier curves with three parameters, to be called adjustable Bézier curves, is constructed. They have the same structure as the quartic Bézier curves. The newly constructed curves possess some of the basic properties of Bézier curves, such as the convex hull property, symmetry, geometri...

A theory of geometric continuity of arbitrary order is presented. Conditions of geometric continuity at a vertex where a number of patches meet are investigated. Geometric continuous patch complexes are introduced as the appropriate setting for the representation of surfaces in CAGD. The theory is applied to the modelling of closed surfaces and the fitting of triangular patches into a geometric...