A bipolar Hardy inequality on Finsler manifolds

Abstract

We establish a bipolar Hardy inequality on complete, not necessarily reversible Finsler manifolds. We show that our result strongly depends on the geometry of the Finsler structure, namely on the reversibility constant $r_F$ and the uniformity constant $l_F$. Our result represents a Finslerian counterpart of the Euclidean multipolar Hardy inequality due to Cazacu and Zuazua (2013) and the Riemannian case considered by Faraci, Farkas and Krist\'aly (2018).