On a sharp Poincar\'e-type inequality on the 2-sphere and its application in micromagnetics

TL;DR

This paper proves a sharp Poincaré-type inequality for vector functions on the 2-sphere, which is relevant for micromagnetics of spherical thin films, providing a mathematical foundation for physical models.

Contribution

It introduces a new sharp Poincaré-type inequality specifically for vector-valued functions on the 2-sphere, with applications in micromagnetics.

Findings

Established a sharp inequality for vector functions on the sphere

Applied the inequality to models in micromagnetics

Enhanced mathematical tools for spherical thin film analysis

Abstract

The main aim of this note is to prove a sharp Poincar\'e-type inequality for vector-valued functions on $\mathbb{S}^2$, that naturally emerges in the context of micromagnetics of spherical thin films.