Related papers: Local bi-Lipschitz classification of semialgebraic…
Let $ \Phi: ({\mathbb C}^2, 0) \to ( {\mathbb C}^3, 0) $ be a finitely determined complex analytic germ and let $(\{f=0\},0)$ be the reduced equation of its image, a non-isolated hypersurface singularity. We provide the plumbing graph of…
In this work, we consider a finitely determined, quasihomogeneous, corank 1 map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We introduce the concept of the $\mu_{\mathbf{m},\mathbf{k}}$-minimal transverse slice of $f$}. Since…
We study an analytically irreducible algebroid germ (X, 0) of complex singularity by considering the filtrations of its analytic algebra, and their associated graded rings, induced by the divisorial valuations associated to the irreducible…
Let $K,F\subset\mathbb{R}^d$ be two dust-like self-similar sets sharing the same Hausdorff dimension. We consider when the mere existence of a Lipschitz embedding from $K$ to $F$ already implies their Lipschitz equivalence. Our main result…
We study the consistency of Lipschitz learning on graphs in the limit of infinite unlabeled data and finite labeled data. Previous work has conjectured that Lipschitz learning is well-posed in this limit, but is insensitive to the…
The article examines a set of irreducible germs $f_P:U_P\to V_p$ of %finite generic morphisms $f:S\to\mathbb P^2$ to the projective plane whose branch curve germs $B_P\subset V_p$ have singularities equisingular deformation equivalent to…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. Actually, the observations show there are two resources to get classification of filiform Leibniz algebras. The first of them…
We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of a bounded selection…
We compare two different types of mapping class invariants: the Hochschild homology of an $A_\infty$ bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. We first compute the bimodule invariants and their…
Let $Crit M$ denote the minimal number of critical points (not necessarily non-degenerate) on a closed smooth manifold $M$. We are interested in the evaluation of $Crit$. It is worth noting that we do not know yet whether $Crit M$ is a…
We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface $M$ in $\C^2$ at a point $p\in M$ are uniquely determined by their jets of some finite order at $p$ if and only if $M$ is not Levi-flat near $p$.…
Consider a sequence of compactly supported Hamiltonian diffeomorphisms $\phi_k$ of an exact symplectic manifold, all of which are "graphical" in the sense that their graphs are identified by a Darboux-Weinstein chart with the image of a…
We investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic…
Two definitions for the rectfiability of hypersurfaces in Heisenberg groups $\mathbb{H}^n$ have been proposed: one based on $\mathbb{H}$-regular surfaces, and the other on Lipschitz images of subsets of codimension-$1$ vertical subgroups.…
Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of…
On a compact connected group $G$, consider the infinitesimal generator $-L$ of a central symmetric Gaussian convolution semigroup $(\mu_t)_{t>0}$. We establish several regularity results of the solution to the Poisson equation $LU=F$, both…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…
The purpose of this paper is the study of the roots in the mapping class groups. Let $\Sigma$ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of $\Sigma$, and let $\MM (\Sigma,…
We investigate the consequence of two Lip$(\gamma)$ functions, in the sense of Stein, being close throughout a subset of their domain. A particular consequence of our results is the following. Given $K_0 > \varepsilon > 0$ and $\gamma >…
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…