Tangencies of generic real projective hypersurfaces.
Tangent sets and differentiable functions
The analytic Carathéodory conjecture.
The analytic domain in the implicit function theorem.
The bounds for the squared norm of the second fundamental form of minimal submanifolds of .
The hypothesis in Pesin theory
The compositions of differential operations and the Gâteaux directional derivative.
The Demyanov metric and some other metrics in the family of convex sets
We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
The Differential Form Spectrum of Hyperbolic Space.
The duals of generic hypersurfaces.
The first eigenvalue of a Riemann surface.
The Gaussian measure on algebraic varieties
We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety is dense in the Hilbert space , where dμ denotes the volume form of M and the Gaussian measure on M.
The generalization of Cellina's Fixed Point Theorem
The Geometry of Critical and Near-Critical Values of Differentiable Mappings.
The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant
Given a real analytic vector field tangent to a hypersurface with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra associated with the singularity of the vector field on . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...
The linking number of singular maps.
The metric regularity of polynomial functions in one or several variables.
The modified analytic trivialization of family of real analytic functions.
The Nash-Moser inverse mapping theorem