Related papers: Quasihomogeneous three-dimensional real analytic L…

We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a polynomially bounded o-minimal structure over the reals, surface germs. In particular, any definable H\"older triangle is either Lipschitz normally…

Any subanalytic germ $(X,0) \subset (\mathbb R^n,0)$ is equipped with two natural metrics: its outer metric, induced by the standard Euclidean metric of the ambient space, and its inner metric, which is defined by measuring the shortest…

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…

Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a…

In this paper, we establish the following criterion for divisibility in the local ring of those quasianalytic function germs at zero which are definable in a polynomially bounded structure. A sufficient (and necessary) condition for the…

We give a classification of superattracting germs in dimension one over a complete normed algebraically closed field of positive characteristic up to conjugacy. In particular we show that formal and analytic classifications coincide for…

We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional…

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or $\CH_3$ for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, $\CH_2$ manifolds that are…

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 notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. A complex analytic…

We give a very simple argument to the effect that most germs of generic real analytic Cauchy-Riemann manifolds of positive CR dimension are not holomorphically embeddable into any generic real algebraic CR manifold of the same real…

We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…

We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian…

We prove that the solutions of a cohomological equation of complex dimension one and in the analytic category have a monogenic dependence on the parameter, and we investigate the question of their quasianalyticity. This equation is the…

We prove under certain conditions that any stable unfolding of a quasi-homogeneous map-germ with finite singularity type is substantial. We then prove that if an equidimensional map-germ is finitely determined, of corank 1, and either it…

T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic…

k-Curvature homogeneous three-dimensional Walker metrics are described for k=0,1,2. This allows a complete description of locally homogeneous three-dimensional Walker metrics, showing that there exist exactly three isometry classes of such…

We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of…

This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…