# Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems

created by braidesa on 27 Oct 2020
modified on 12 Jan 2021

[BibTeX]

Accepted Paper

Inserted: 27 oct 2020
Last Updated: 12 jan 2021

Journal: COCV
Year: 2021

Abstract:

We prove two geometric lemmas for $S^{N-1}$-valued functions that allow to modify sequences of lattice spin functions on a small percentage of nodes during a discrete-to-continuum process so as to have a fixed average. This is used to simplify known formulas for the homogenization of spin systems.