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.
Packing dimensions, transversal mappings and geodesic flows.
Parametric representations of semi-complete vector fields on the unit balls in and in Hilbert space
We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.
Periodic points and rotation numbers for area preserving diffeomorphisms of the plane
Periodic segments and Nielsen numbers
We prove that the Poincaré map has at least fixed points (whose trajectories are contained inside the segment W) where the homeomorphism is given by the segment W.
Periodic solutions to Maxwell equations in nonlinear media
Periods for holomorphic maps via Lefschetz numbers.
Perturbing away singularity from area-minimizing hypercones.