Minimal Networks on Balls and Spheres for Almost Standard Metrics.

We study the existence of minimal networks in the unit sphere S d and the unit ball B d of R d endowed with Riemannian metrics close to the standard ones. We employ a finite-dimensional reduction method, modelled on the configuration of θ -networks in S d and triods in B d , jointly with the Lusternik–Schnirelmann category. [ABSTRACT FROM AUTHOR]