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math.DG2023
Nonlocal approximation of minimal surfaces: optimal estimates from stability
Hardy Chan, Serena Dipierro, Joaquim Serra +1
Minimal surfaces in closed 3-manifolds are classically constructed via the Almgren-Pitts approach. The Allen-Cahn approximation has proved to be a powerful alternative, and Chodosh…
math.DG2023
Yau's conjecture for nonlocal minimal surfaces
Michele Caselli, Enric Florit-Simon, Joaquim Serra
We introduce nonlocal minimal surfaces on closed manifolds and establish a far-reaching Yau-type result: in every closed, -dimensional Riemannian manifold we construct infinitel…