14 citations · 14 across the 3 of their papers we have counts for
4 papers
Anisotropic min-max via phase transitions
Antonio De Rosa, Alessandro Pigati
We develop a PDE-based approach to the min-max construction of nontrivial integer rectifiable varifolds that are stationary with respect to anisotropic surface energies on closed R…
A Variational Theory for The Area of Legendrian Surfaces
Alessandro Pigati, Tristan Rivière
We study a new notion of critical point for the area of surfaces under the Legendrian constraint, called parametrized Hamiltonian stationary Legendrian varifolds (PHSLVs). We estab…
A proof of the multiplicity one conjecture for min-max minimal surfaces in arbitrary codimension
Alessandro Pigati, Tristan Rivière
Given any admissible -dimensional family of immersions of a given closed oriented surface into an arbitrary closed Riemannian manifold, we prove that the corresponding min-max w…
The regularity of parametrized integer stationary varifolds in two dimensions
Alessandro Pigati, Tristan Rivière
We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion…