English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The real homology of a compact Riemannian manifold $M$ is naturally endowedwith the stable norm. The stable norm on $H_1(M,\mathbb{R})$ arises from theRiemannian length functional by homogenization. It is difficult and interestingto decide which norms on the finite-dimensional vector space$H_1(M,\mathbb{R})$ are stable norms of a Riemannian metric on $M$. If thedimension of $M$ is at least three, I. Babenko and F. Balacheff proved in\cite{baba} that every polyhedral norm ball in $H_1(M,\mathbb{R})$, whosevertices are rational with respect to the lattice of integer classes in$H_1(M,\mathbb{R})$, is the stable norm ball of a Riemannian metric on $M$.This metric can even be chosen to be conformally equivalent to any givenmetric. The proof in \cite{baba} uses singular Riemannian metrics on polyhedrawhich are finally smoothed. Here we present an alternative construction of suchmetrics which remains in the geometric framework of smooth Riemannian metrics.

Hedlund-Metrics and the Stable Norm