Differentiability of the stable norm in codimension one

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dc.creatorAuer, Franz
dc.creatorBangert, Victor
dc.date2004-03-15
dc.date2004-12-03
dc.date.accessioned2026-07-07T05:06:24Z
dc.date.available2026-07-07T05:06:24Z
dc.descriptionThe real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on H_{n-1}(M,R) is a homogenized version of the Riemannian (n-1)-volume. We study the differentiability properties of the stable norm at points alpha in H_{n-1}(M,R). They depend on the position of alpha with respect to the integer lattice H_{n-1}(M,Z) in H_{n-1}(M,R). In particular, we show that the stable norm is differentiable at alpha if alpha is totally irrational.
dc.description28 pages LaTeX. Submitted to American Journal of Mathematics; Reference added. Minor inaccuracy corrected; Revised version for publication after referee report. Proof of Propositon 2.4 added. Some inaccuracies corrected and some unclear formulations changed
dc.identifierhttps://arxiv.org/abs/math/0403235
dc.identifierhttp://arxiv.org/abs/math/0403235
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70457
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject49Q20 (Primary) 35B27, 53C38 (Secondary)
dc.titleDifferentiability of the stable norm in codimension one
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