Minimization of Anisotropic Energies in Classes of Rectifiable Varifolds

Source abstract

We consider the minimization problem of an anisotropic energy in classes of $d$-rectifiable varifolds in $\mathbb{R}^n$, closed under Lipschitz deformations and encoding a suitable notion of boundary. We prove that any minimizing sequence with density uniformly bounded from below converges (up to subsequences) to a $d$-rectifiable varifold. Moreover, the limiting varifold is integral, provided all the elements of the minimizing sequence are integral varifolds with uniformly locally bounded anisotropic first variation.