Related papers: Bi-H"older invariants in o-minimal structures

Let $M$ be a real analytic hypersurface in $\bC^N$ which is finitely nondegenerate, a notion that can be viewed as a generalization of Levi nondegenerate, at $p_0\in M$. We show that if $M'$ is another such hypersurface and $p'_0\in M'$,…

We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…

We study the Siegel--Schr\"oder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey--$s$, $s>0$ category. We introduce a new arithmetical condition of Bruno type on the linear…

We consider the Riemann Mapping Theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (i.e. biholomorphic map) from the upper half plane to such a domain can be realized in…

A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if a countable theory T has the Schroder-Bernstein property then it is classifiable (it is…

We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of na irreducible hypersurface in the complex projective…

Let G a group of germs of analytic diffeomorphisms in (C^2,0). We find some remarkable properties supposing that G is finite, linearizable, abelian nilpotent and solvable. In particular, if the group is abelian and has a generic dicritic…

This paper is the first one of two papers whose goal is to give a converse to the main result of my previous paper [6], so to prove the existence of multiple poles for the distribution |f|2$\lambda$ with an hypothesis on a Higher Bernstein…

Let $f$ be a germ of holomorphic diffeomorphism with an irrationally indifferent fixed point at the origin in $\mathbb{C}$ (i.e. $f(0) = 0, f'(0) = e^{2\pi i \alpha}, \alpha \in \mathbb{R} - \mathbb{Q}$). Perez-Marco showed the existence of…

Let $X$ be a compact connected Riemann surface of genus at least two. The main theorem of arxiv:1010.1488 says that for any positive integer $n \leq 2({\rm genus}(X)-1)$, the symmetric product $S^n(X)$ does not admit any K\"ahler metric…

Given a semianalytic set S in a complex space and a point p in S, there is a unique smallest complex-analytic germ at p which contains the germ of S, called the holomorphic closure of S at p. We show that if S is semialgebraic then its…

The image of a finitely determined holomorphic germ $\Phi$ from $\mathbb{C}^2$ to $\mathbb{C}^3$ defines a hypersurface singularity $(X,0)$, which is in general non-isolated. We show that the diffeomorphism type of the boundary of the…

We prove that a (branched) minimal immersion from $\mathbb{C}$ to $\mathbb{R}^n$ is stable if and only if it lives in an even dimensional affine subspace and is holomorphic for some orthogonal complex structure on the subspace. More…

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…

Let M be a closed 5-manifold of pinched curvature 0<\delta\le \text{sec}_M\le 1. We prove that M is homeomorphic to a spherical space form if M satisfies one of the following conditions: (i) \delta =1/4 and the fundamental group is a…

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~$k$ (i.e.~a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on $k$ real…

The classification, by topological conjugacy, of invertible holomorphic germs $f:(\mathbb{C}^n,0)\to (\mathbb{C}^n,0)$, with $\lambda_1,...,\lambda_n$ eigenvalues of $df_0$, and $|\lambda_i|\neq 1$ for $i=2,...,n$ while $\lambda_1$ is a…

Corollary: Two germs of minimal real analytic CR-generic manifolds are formally equivalent if and only if they are biholomorphic.

We prove a conjecture of Kim and Oum that every proper pivot-minor-closed class of graphs has the strong Erd\H{o}s-Hajnal property. More precisely, for every graph $H$, there exists $\epsilon > 0$ such that every $n$-vertex graph with no…

In this paper, we consider the normal form problem of a commutative family of germs of diffeomorphisms at a fixed point, say the origin, of $\mathbb{K}^n$ ($\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$). We define a notion of integrability of…