Makover, Eran Parlier, Hugo Sutton, Craig J. 2012-03-13 A result of Bangert states that the stable norm associated to any Riemannian metric on the 2-torus <em>T</em> ² is strictly convex. We demonstrate that the space of stable norms associated to metrics on <em>T</em> ² forms a proper dense subset of the space of strictly convex norms on R2{/span> . In particular, given a strictly convex norm || · ||_∞ on R2{/span> we construct a sequence ⟨∥⋅∥j⟩∞j=1{/span> of stable norms that converge to || · ||_∞ in the topology of compact convergence and have the property that for each <em>r</em> > 0 there is an N≡N(r){/span> such that || · ||_<em>j</em>agrees with || · ||_∞ on Z2∩{(a,b):a2+b2≤r}{/span> for all <em>j</em> ≥ <em>N</em>. Using this result, we are able to derive results on multiplicities which arise in the minimum length spectrum of 2-tori and in the simple length spectrum of hyperbolic tori. application/pdf https://folia.unifr.ch/global/documents/302721 https://folia.unifr.ch/documents/302721/files/par_cmt.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-012-0538-1 info:eu-repo/semantics/openAccess License undefined Manuscripta Mathematica. - 2012, vol. 139, no. 3-4, p. 515-534 info:eu-repo/classification/udc/51 Constructing metrics on a 2-torus with a partially prescribed stable norm http://purl.org/coar/resource_type/c_6501