Published in Mathematische Zeitschrift
We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds’ lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral weight to meromorphic modular forms of even integral weight having poles at CM points.
Published in Mathematische Zeitschrift
We study rigidity properties of lattices in terms of invariant means and commensurating actions (or actions on CAT(0) cube complexes). We notably study Property FM for groups, namely that any action on a discrete set with an invariant mean has a finite orbit.
Published in Mathematische Zeitschrift
A Laguerre minimal surface is an immersed surface in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^3}$$\end{document} being an extremal of the functional ...
Published in Mathematische Zeitschrift
Building on results of Ando, Hopkins and Rezk, we show the existence of uncountably many E∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {E}}_\infty $$\end{d...
Published in Mathematische Zeitschrift
A well known result of Mazur gives a lower bound for the Krull dimension of the universal deformation ring associated to an absolutely irreducible residual representation in terms of the group cohomology of the adjoint representation. The question about equality — at least in the Galois case — also goes back to Mazur. In the general case the questi...
Published in Mathematische Zeitschrift
We study the asymptotic Dirichlet and Plateau problems on Cartan–Hadamard manifolds satisfying the so-called strict convexity (abbr. SC) condition. The main part of the paper consists in studying the SC condition on a manifold whose sectional curvatures are bounded from above and below by certain functions depending on the distance to a fixed point...
Published in Mathematische Zeitschrift
We study heights of subspaces of DN where D is a finite-dimensional rational division algebra and N a positive integer. We define them in terms of volumes of Euclidean lattices by extending a formula of W. Schmidt so that we recover the classical height if D is commutative. We review basic properties, prove a Siegel Lemma over D, a duality theorem ...
Published in Mathematische Zeitschrift
In this article weakly isotropic quadratic forms over a (formally) real field are studied. Conditions on the field are given which imply that every weakly isotropic form over that field has a weakly isotropic subform of small dimension. Fields over which every quadratic form can be decomposed into an orthogonal sum of a strongly anisotropic form an...
Published in Mathematische Zeitschrift
Using a cohomological obstruction, we construct examples of absolutely simple adjoint classical groups of type 2An with n≡3mod4, Cn or 1Dn with n≡0mod4, which are not R-trivial hence not stably rational.
Published in Mathematische Zeitschrift
In analogy to a characterisation of operator matrices generating C0-semigroups due to R. Nagel ([13]), we give conditions on its entries in order that a 2×2 operator matrix generates a cosine operator function. We apply this to systems of wave equations, to second order initial-boundary value problems, and to overdamped wave equations.
