Geometric Analysis and Topology Seminar

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Rigidity and non-rigidity of the stable norm on $T^n$

Speaker: Ao Sun, Lehigh University

Location: Online

Videoconference link: https://nyu.zoom.us/j/96390398010

Date: Friday, October 2, 2026, 11 a.m.

Synopsis:

The stable norm, introduced by Federer, is the extension of the area of minimizing surfaces in integer homology classes to the real homology classes. We show that the stable norm of flat metrics on $H_d(T^n,R)$ is locally rigid if $1\leq d<n-1$ and locally rigid among metrics of the same volume if $d=n-1$. This result shows that the area of homologically minimizing surfaces can determine the flat metrics on the torus locally. The motivation and idea are broadly connected to minimal surface theory, geometric measure theory, dynamical systems, Fourier analysis, and homogenization theory. Based on joint work with Fernando Codá Marques and André Neves.