Differentialgeometrie der Kugel- und Linienmannigfaltigkeiten im dreidimensionalen euklidischen Raum
Differentialgeometrie der -dimensionalen Kugel- und Linienmannigfaltigkeiten im -dimensionalen euklidischen Raum
Differentialgeometrie der zweidimensionalen Kugel- und Linienmannigfaltigkeiten im dreidimensionalen Euklidischen Raum. I.
Differentialgeometrie der zweidimensionalen Kugel- und Linienmannigfaltigkeiten im dreidimensionalen Euklidischen Raum. II.
Dirac and Plateau billiards in domains with corners
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry,...
Direct kinematics of double-triangular parallel manipulators.
Discrete and nondiscrete isometric deformations of surfaces in .
Discrete isothermic surfaces.
Discrete Laplace cycles of period four
We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.
Discrete minimal surface algebras.
Discrete thickness
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies...
Discrétisation de zeta-déterminants d’opérateurs de Schrödinger sur le tore
Nous donnons ici deux résultats sur le déterminant -régularisé d’un opérateur de Schrödinger sur une variété compacte . Nous construisons, pour , une suite où est un graphe fini qui se plonge dans via de telle manière que soit une triangulation de et où est un laplacien discret sur tel que pour tout potentiel sur , la suite de réels converge après renormalisation vers . Enfin, nous donnons sur toute variété riemannienne compacte de dimension inférieure ou égale à ...
Discussion de l'intersection de deux surfaces du second ordre
Discussion de l'intersection de deux surfaces du second ordre
Distinguished connections on -metric manifolds
We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...
D-modules et geometrie des tissus de C2.
Double bubbles in the three-torus.
Double bubbles minimize.
Double points on characteristics
Double Points on Characteristics. A fixed surface of a moving space will envelope a surface of the fixed space , if we move with respect to . In the general case at each moment of the one-parameter motion there exists a curve on , along which the position of and the enveloped surface are in contact. In the paper we study the interesting special case, where has some double point . This depends on relations between differential geometric properties in the neighbourhood of of the...
Doubling constant mean curvature tori in S
The Clifford tori in constitute a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled catenoid...