We are thrilled to announce that our Professor Antonio De Rosa has published an outstanding article titled "On the Theory of Anisotropic Minimal Surfaces" in the prestigious Notices of the American Mathematical Society, the world's most widely read mathematical journal. This article reviews the groundbreaking results established by Antonio De Rosa at the foundation of the theory of anisotropic minimal surfaces. De Rosa's work delves into the complex nature of anisotropic minimal surfaces and their significant implications in the field of geometric measure theory.

Why is this study important?

Anisotropic minimal surfaces minimize a directionally dependent energy functional, unlike isotropic minimal surfaces which minimize the area functional. These surfaces model natural phenomena where surface tension varies with the orientation of the surfaces, such as crystalline structures, capillarity models and soap films. The complexity in analyzing anisotropic minimal surfaces arises because they do not enjoy the same conservation laws as isotropic minimal surfaces, making their existence and regularity more challenging to study.

De Rosa's work gives a positive answer to longstanding conjectures in the broad field of geometric measure theory, such as the conjecture posed by the renowned mathematician William K. Allard in 1983 on the min-max construction of closed optimally regular anisotropic minimal hypersurfaces in closed Riemannian manifolds.