Differentiability of the stable norm in codimension one
Franz Auer, Victor Bangert
Abstract
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.
Create a lesson
Related papers
Topological and spectral rigidity of hypersurface Zoll manifolds
Gustavo Martins
Stationary varifolds with singularities II
Camillo De Lellis, Jonas Hirsch, Zachary Lihn et al.
Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities
Mitchell Gaudet
Deformations of harmonic maps with conical singularities
Dominik Gutwein, Thibault Langlais
The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds
Shibing Chen, Mohammad Ghomi, Peng Wang
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song