2004/03/15 by Franz Auer, Auer, Franz, Victor Bangert +1
Mathematics · Physics and Astronomy · #49Q20 (Primary) 35B27 #53C38 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.AP #math.DG #msc:35B27 #msc:49Q20 #msc:53C38
paper · pdf · doi:10.48550/arxiv.math/0403235
28 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
openalex publication_date 2004/03/15 · arxiv created 2004/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 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 Hn-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 Hn-1(M,R). They depend on the position of alpha with respect to the integer lattice Hn-1(M,Z) in Hn-1(M,R). In particular, we show that the stable norm is differentiable at alpha if alpha is totally irrational.