arXiv subjects

V. Schroeder

Publications and source records attributed to V. Schroeder.

4 recordsLinked to original sources

arXiv2016

Moebius rigidity of invariant metrics in boundaries of symmetric spaces of rank 1

Let $\partial{\bf H}^n_{\mathbb K}$ denote the boundary of a symmetric space of rank-one and of non-compact type and let $d_{\mathfrak{H}}$ be the Korányi metric defined in $\partial{\bf H}^n_{\mathbb K}$. We prove that if $d$ is a metric on $\partial{\bf H}^n_{\mathbb K}$ such that all Heisenberg similarities are $d$-Möbius maps, then under a topological condition $d$ is a constant multiple of a power of $d_{\mathfrak{H}}$.

math.MG↗

arXiv2004

Hyperbolic dimension of metric spaces

We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^n is zero (while asdim R^n=n.) This invariant possesses usual properties of dimension like monotonicity and product theorems. Our main result says that the hyperbolic dimension of any Gromov hyperbolic space X (with mild restrictions) is at least the topological dimension of the boundary at infinity plus 1. As an application we obtain that there is no quasi-isometric embedding of the real hyperbolic space H^n into the (n-1)-fold metric product of metric trees stabilized by any Euclidean factor.

math.GT↗

arXiv2003

Embedding of hyperbolic spaces in the product of trees

We show that for each n\ge 2 there is a quasi-isometric embedding of the hyperbolic space H^n in the product T^n=Tx...xT of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding H^2 --> TxR^m for any metric tree T and any m\ge 0.

math.GT↗

arXiv2000

The H1 Forward Proton Spectrometer at HERA

The forward proton spectrometer is part of the H1 detector at the HERA collider. Protons with energies above 500 GeV and polar angles below 1 mrad can be detected by this spectrometer. The main detector components are scintillating fiber detectors read out by position-sensitive photo-multipliers. These detectors are housed in so-called Roman Pots which allow them to be moved close to the circulating proton beam. Four Roman Pot stations are located at distances between 60 m and 90 m from the interaction point.

hep-ex↗