Symmetry groups and conservation laws of certain partial differential equations.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry of local minimizers for the three-dimensional Ginzburg–Landau functional
We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.
Symmetry of the barochronous motions of a gas.
Symmetry of the Ginzburg-Landau minimizer in a disc
Symmetry operators of a Hartree-type equation with quadratic potential.
Symplectic critical surfaces in Kähler surfaces
Let be a Kähler surface and be a closed symplectic surface which is smoothly immersed in . Let be the Kähler angle of in . We first deduce the Euler-Lagrange equation of the functional in the class of symplectic surfaces. It is , where is the mean curvature vector of in , is the complex structure compatible with the Kähler form in , which is an elliptic equation. We call such a surface a symplectic critical surface. We show that, if is a Kähler-Einstein surface with nonnegative...
Symplectic Killing spinors
Let be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection . Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one may easily...
Symplectic rigidity of geodesic flows on two-step nilmanifolds
Symplectic spinor valued forms and invariant operators acting between them
Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.
Systeme von Differentialgleichungen Erster Ordnung vom Elliptischen Typus mit Analytischen Koeffizienten und Methode der Verallgemeinerten Areolaren Reihen
Systèmes différentiels à caractéristiques simples et structures réelles-complexes
Systems of meromorphic microdifferential equations
We introduce the notion of system of meromorphic microdifferential equations. We use it to prove a desingularization theorem for systems of microdifferential equations.
Tetra and Didi, the cosmic spectral twins.
The abstract Riemannian path space.
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...
The analytic Carathéodory conjecture.
The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces.
The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry.