Related papers: Ping-Pong on Negatively Curved Groups

We present new mathematical alternatives for explaining rotation curves of spiral galaxies in the MOND context. For given total masses, it is shown that various mathematical alternatives to MOND, while predicting flat rotation curves for…

The goal of this paper is to present a number of problems about automorphism groups of nonpositively curved polyhedral complexes and their lattices, meant to highlight possible directions for future research.

Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric…

We prove a version of van der Corput's Lemma for polynomials over the p-adic numbers.

We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by…

In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of…

We classify real and complex infinite-dimensional narrow positively graded Lie algebras ${\mathfrak g}=\oplus_{i=1}^{{+}\infty}{\mathfrak g}_i$ with properties $$ [{\mathfrak g}_1, {\mathfrak g}_i]={\mathfrak g}_{i{+}1}, \; \dim{{\mathfrak…

Under mild assumptions on a group G, we prove that the class of complete Riemannian n-manifolds of uniformly bounded negative sectional curvatures and with the fundamental groups isomorphic to G breaks into finitely many tangential homotopy…

The purpose of this article is to present a "Groupoid proof" to the Lefschetz fixed point formula for elliptic complexes. We shall define a "relative version" of tangent groupoid, describe the corresponding pseudodifferential calculi and…

We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.

In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the…

We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that…

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

We prove a local-global principle for torsors under the prosolvable geometric fundamental group of an affine curve over a number field.

In this paper we prove a quantitative closing Lemma for manifolds of negative sectional curvature. As an application we study partner and pseudo-partner orbits for self-crossing closed geodesic.

We refine and extend quantitative bounds, on the fraction of nonnegative polynomials that are sums of squares, to the multihomogenous case.

We generalize Demailly's construction of projective jet bundles and strictly negatively curved pseudometrics on them to the logarithmic case. We establish this logarithmic generalization explicitly via coordinates, just as Noguchi's…

In this article I define and study the overconvergent rigid fundamental group of a variety over an equicharacteristic local field. This is a non-abelian $(\varphi,\nabla)$-module over the bounded Robba ring $\mathcal{E}_K^\dagger$, whose…

A Mumford group is a discontinuous subgroup $\Gamma$ of PGL(2,K), where K denotes a non archimedean valued field, such that the quotient by $\Gamma$ is a curve of genus 0. As abstract group $\Gamma$ is an amalgam of a finite tree of finite…