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math.DG2026
Min-Max Construction of Anisotropic Minimal Surfaces with Genus Bound
Antonio De Rosa, Aria Halavati, Ling Wang
We establish an anisotropic analogue of the celebrated theorem of Meeks-Simon-Yau: every minimizing sequence of surfaces within a fixed isotopy class converges to a smooth stable a…
math.DG2025
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…
math.DG2024
Existence and regularity of min-max anisotropic minimal hypersurfaces
Guido De Philippis, Antonio De Rosa, Yangyang Li
In any closed smooth Riemannian manifold of dimension at least three, we use the min-max construction to find anisotropic minimal hyper-surfaces with respect to elliptic integrands…