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We consider foliations on a germ of an isolated surface singularity. We give criteria for the existence of smooth separatrices in terms of the maximal cycle of a desingularization of the surface. We apply these criteria for some examples of quasi-homogeneous singularities, in particular rational...
After obtaining an explicit description in coordinates of invariant metrics on four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds, for each of these spaces we completely describe Killing and geodesic vector fields and homogeneous geodesics through a point. In particular, this...
A local expression of the Diederich-Fornaess exponent of complements of Levi-flat real hypersurfaces is exhibited. This expression describes the correspondence between pseudoconvexity of their complements and positivity of their normal bundles, which was suggested in a work of Brunella, in a...
We introduce the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. The latter refers to the existence of (unique) bounded solutions for any bounded perturbation of the original dynamics. We...
We obtain a condition, involving geodesics orthogonal to tangent vectors, which implies that a submanifoldmust be contained in a level set of a Lipschitz function. One application is the following theorem. Let f : Σ → M be a differentiable immersion of a connected manifold Σ in a complete...
The proof of norm resolvent convergence of Dirichlet Laplacian to effective operators, as the diameter of spatial waveguides vanishes, is extended to the unbounded case.
In our original paper , Theorem 2.1 of , that we quoted, was not properly proved. This was done by Lee-Louboutin . The gap doesn’t affect the final result of the paper.
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