Constructing metrics on a 2-torus with a partially prescribed stable norm
- Makover, Eran Department of Mathematics, Central Connecticut State University, New Britain, USA
- Parlier, Hugo Department of Mathematics, University of Fribourg, Switzerland
- Sutton, Craig J. Department of Mathematics, Dartmouth College, Hanover, USA
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13.03.2012
Published in:
- Manuscripta Mathematica. - 2012, vol. 139, no. 3-4, p. 515-534
English
A result of Bangert states that the stable norm associated to any Riemannian metric on the 2-torus T ² is strictly convex. We demonstrate that the space of stable norms associated to metrics on T 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 r > 0 there is an N≡N(r){/span> such that || · || j agrees with || · ||∞ on Z2∩{(a,b):a2+b2≤r}{/span> for all j ≥ N. 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.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 30991
- DOI 10.1007/s00229-012-0538-1
- Persistent URL
- https://folia.unifr.ch/unifr/documents/302721
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