Differential spaces and singularities of space-time.
Differential Topology and the Computation of Total Absolute Curvature.
Differential-geometric and variational background of classical gauge field theories.
Differential-geometrical conditions between geodesic curves and ruled surfaces in the Lorentz space.
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.
Diffuse-interface treatment of the anisotropic mean-curvature flow
We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.
Dilations associated to flat curves.
I would like to give an exposition of the recent work of Tony Carbery, Mike Christ, Jim Vance, David Watson and myself concerning Hilbert transforms and Maximal functions along curves in R2 [CCVWW].
Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the...
Dimers and cluster integrable systems
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs and areequivalentif the Newton polygons of the corresponding partition functions...
Dipolarizations in semisimple Lie algebras and homogeneous parakähler manifolds.
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,...
Dirac brackets in geometric dynamics
Dirac field on newtonian space-time
Dirac operator in contact symplectic parabolic geometry
Dirac operators on hypersurfaces
In this paper some relation among the Dirac operator on a Riemannian spin-manifold , its projection on some embedded hypersurface and the Dirac operator on with respect to the induced (called standard) spin structure are given.
Dirac structures and dynamical -matrices
The purpose of this paper is to establish a connection between various objects such as dynamical -matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the theory of Dirac structures and Courant algebroids. In particular, we give a new method of classifying dynamical -matrices of simple Lie algebras , and prove that dynamical -matrices are in one-one correspondence with certain Lagrangian subalgebras of .
Dirac submanifolds and Poisson involutions