Differential modules
Differential operators and -structures of higher order
Differential operators cononically associated to a conformal structure.
Differential Operators on Homogeneous Spaces. I. Irreducibility of the Associated Variety for Annihilators of Induced Modules.
Differential operators on homogeneous spaces. II : relative enveloping algebras
Differential pseudoconnections and field theories
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,...