Möbius invariants for pairs of spheres in the Möbius space .
Möbiussche Bewegungen der Ebene mit mehrfach durchlaufenen Bahnkurven
Im Artikel wird eine spezielle Klasse der Möbiusschen Bewegungen der Ebene, die so gegeben werden, daß eine gewisse Punktfolge in gleichen Zeitintervallen dieselbe Bahnkurve durchläuft, studiert. Die Bestimmung dieser Bewegungen führt zur Lösung eines im allgemeinen nichtlinearen Systems von Differenzengleichungen. Im Artikel wird eine Unterklasse dieser Bewegungen, die durch die Lösung eines speziellen linearen Systems der Differenzengleichungen festgestellt wird, studiert. Dessen Lösung führt...
Modeling repulsive forces on fibres via knot energies
Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having...
Modules pour les familles de courbes planes
L’étude des familles de courbes plane différentiables se ramène a celle des diagrammesoù est une surface, et étant différentiables. Dans la classification de ces diagrammes à équivalence près il apparaît trois types de modules: des modules locaux attachés à chaque fronce de , des modules semi-locaux attachés à la superposition en un même point de plusieurs situations locales, des modules globaux attachés aux “courbes de contact” le long desquelles certaines courbes sont tangentes. Nous explicitons...
Moduli of half conformally flat structures.
Monge-Ampère Equations, Geodesics and Geometric Invariant Theory
Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also discussed....
Morales-Ramis Theorems via Malgrange pseudogroup
In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.
More on the Determinacy of Smooth Map-Germs.
Motion by curvature of planar networks
We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two–dimensional multiphase system where the energy is simply the sum of the lengths of the interfaces, in particular it is a possible model for the growth of grain boundaries. Moreover, the motion of these networks of curves is the simplest example of curvature flow for sets which...
Motions in the flag space with spherical trajectories. I: The four-parametric motions. (Bewegungsvorgänge des Flaggenraumes mit sphärischen Bahnen. I: Die vierparametrigen Bewegungsvorgänge.)
Motions in the flag space with spherical trajectories. II: The three-parametric motions. (Bewegungsvorgänge des Flaggenraumes mit sphärischen Bahnen. II: Die dreiparametrigen Bewegungsvorgänge.)
Multi-helicoidal Euclidean submanifolds of constant sectional curvature.
Multilocal invariants for the classical groups.
Multiple convex hypersurfaces with prescribed mean curvature
Multiple surfaces of non-constant mean curvature.