Naumann, Niko Sprang, Johannes
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...

Sprang, Johannes
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...

Casteras, Jean-Baptiste Holopainen, Ilkka Ripoll, Jaime B.
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...

Liebendörfer, Christine Rémond, Gaël
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 ...

Becher, Karim Johannes
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...

Berhuy, Grégory Monsurrò, Marina Tignol, Jean-Pierre
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.

Mugnolo, Delio
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.

Paşol, Vicenţiu Zaharescu, Alexandru
Published in
Mathematische Zeitschrift

In their study of diophantine approximation of the exponential function in connection with Sondow’s Conjecture, Berndt et al. (Adv Math 348:1298–1331, 2013) have constructed certain p-adic functions arising from the sequence of convergents to the continued fraction of e. We solve an open problem posed in [2], more precisely we show that those p-adi...

Parab, Abhishek
Published in
Mathematische Zeitschrift

We show that the distributions occurring in the geometric and spectral side of the twisted Arthur–Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven when the group is split. The result extends the work of Finis–Lapid (and Müller, spectral side) to the twisted...

Impera, Debora Rimoldi, Michele
Published in
Mathematische Zeitschrift

We obtain a quantitative estimate on the generalised index of translators for the mean curvature flow with bounded norm of the second fundamental form. The estimate involves the dimension of the space of weighted square integrable f-harmonic 1-forms. By the adaptation to the weighted setting of Li–Tam theory developed in previous works, this yields...