On the Lie algebra of vertical prolongation operators
On the local structure of a generic central set
On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator
In the present work, using a formula describing all scalar spectral functions of a Carleman operator of defect indices in the Hilbert space that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator .
On the minima of functionals with linear growth
On the multiplicity of eigenvalues of conformally covariant operators
Let be a compact Riemannian manifold and an elliptic, formally self-adjoint, conformally covariant operator of order acting on smooth sections of a bundle over . We prove that if has no rigid eigenspaces (see Definition 2.2), the set of functions for which has only simple non-zero eigenvalues is a residual set in . As a consequence we prove that if has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics in the -topology....
On the Order of Determination of a Finitely Determined Germ.
On the Pham example and the universal topological stratification of singularities
On the radius of a set in a Hilbert space
On the range of the derivative of a smooth function and applications.
We survey recent results on the structure of the range of the derivative of a smooth real valued function f defined on a real Banach space X and of a smooth mapping F between two real Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of L(X,Y) for the existence of a Fréchet-differentiable mapping F from X into Y so that F'(X) = A. Whenever F is only assumed Gâteaux-differentiable, new phenomena appear: we discuss the existence of a mapping F...
On the regularity of solutions in Convex Integration theory.
On the Size of Balls Covered by Analytic Transformations.
On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy.
On the symmetry of Stokes regions of a simple singularity.
On the tangency of multifunctions
On the uniqueness of the -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.
On the uniqueness of the fixed point index on differentiable manifolds.
On topological degree and Poincaré duality
In this Note we investigate about some relations between Poincaré dual and other topological objects, such as intersection index, topological degree, and Maslov index of Lagrangian submanifolds. A simple proof of the Poincaré-Hopf theorem is recalled. The Lagrangian submanifolds are the geometrical, multi-valued, solutions of physical problems of evolution governed by Hamilton-Jacobi equations: the computation of the algebraic number of the branches is showed to be performed by using Poincaré dual....
On Topological Stability of Divergent Diagrams of Folds.
On totally umbilical cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra
Optimality conditions for problems with set-valued objectives.