Related papers: A bi-Lipschitz invariant for analytic function ger…
By combining analytic and geometric viewpoints on the concentration of the curvature of the Milnor fibre, we prove that Lipschitz homeomorphisms preserve the zones of multi-scale curvature concentration as well as the gradient canyon…
We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation…
To any Nash germ invariant under right composition with a linear action of a finite group, we associate its equivariant zeta functions, inspired from motivic zeta functions, using the equivariant virtual Poincar\'e series as a motivic…
In this work, we extend the concept of the double of an ideal defined in \cite{G2}, to the context of modules. We also obtain the genericity of the infinitesimal Lipschitz condition A for an enlarged class of analytic spaces.
Earlier, for an action of a finite group $G$ on a germ of an analytic variety, an equivariant $G$-Poincar\'e series of a multi-index filtration in the ring of germs of functions on the variety was defined as an element of the Grothendieck…
We show that for $0<\gamma, \gamma' <1$ and for measurable subsets of the unit square with Lebesgue measure $\gamma$ there exist bi-Lipschitz maps with bounded Lipschitz constant (uniformly over all such sets) which are identity on the…
In this paper, we derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function in several variables. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
We observe that a function on a group equipped with a bi-invariant word metric is Lipschitz if and only if it is a partial quasimorphism bounded on the generating set. We also show that an undistorted element is always detected by an…
To a multi-index filtration (say, on the ring of germs of functions on a germ of a complex analytic variety) one associates several invariants: the Hilbert function, the Poincar\'e series, the generalized Poincar\'e series, and the…
We give the general form for a germ of holonomic distribution of one complex variable.
This object of this paper to give several properties and applications of multiple p-adic q-L-function of two variables.
An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Nowadays, most Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this…
We provide radial variational estimates for positive harmonic functions on Lipschitz domains in higher dimensions. The intention of this paper is to document an updated and refined version of arXiv:2003.07176 which modifies the proof of…
The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with…
To a Nash function germ, we associate a zeta function similar to the one introduced by J. Denef and F. Loeser. Our zeta function is a formal power series with coefficients in the Grothendieck ring $\mathcal{M}$ of $\mathcal{AS}$-sets up to…
In this note, we consider generalizations of the asymptotic Hopf invariant, or helicity, for Hamiltonian systems with one-and-a-half degrees of freedom and symplectic diffeomorphisms of a two-disk to itself.
We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.