The elliptical and hyperbolic outcrop patterns characteristic of periclinal folds can be used to classify structures according to different curvature attributes. Elliptical patterns indicate domalbasinal structures with synclastic curvature, that is, principal curvatures of the same sign. Hyperbolic patterns are diagnostic of anticlastic curvature (saddle-like structures). Such outcrop geometri...

We discuss the Siciak-Zaharjuta extremal function of a real convex body in Cn, a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphic ...

We discuss the Siciak-Zaharjuta extremal function of a real convex body in C n , a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphi...

We introduce two natural notions for the occupation measure of a function V with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show that both measures are absolutely continuous with respect to the Lebesgue measure. Occupation densities can be thought of as local times of V , and are descri...

We apply the penalty method to the curve straightening flow of inextensible planar open curves generated by the Kirchhoff bending energy. Thus we consider the curve straightening flow of extensible planar open curves generated by a combination of the Kirchhoff bending energy and a functional penalising deviations from unit arc-length. We start with the governing equations of the explicit parame...

Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed by use of the discrete dipole approximation (DDA) and scanning flow cytometry (SFC), respectively. SFC permits measurement of the angular dependence of the light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scat...

We present an augmented reality application which introduces differential geometry in educational dynamic geometry software. New functionality such as a Frenet frame, center and circle of curvature in arbitrary curve points, and others were implemented. Dynamic geometry allows to study differential geometric properties under movement. Using this tool we developed examples which enable teachers ...