Antonio De Rosa Achieves Top Distinction
Antonio De Rosa, of Bocconi’s Department of Decision Sciences, has had an article published in the August 2024 issue of Notices of the American Mathematical Society (AMS), a leading organization for mathematicians. This publication is a significant accomplishment and confirms the value of Antonio's important research contributions to the field of geometric analysis.
The article, titled "On the Theory of Anisotropic Minimal Surfaces" (you can find it here), reviews Antonio’s broader study of anisotropic minimal surfaces. Antonio De Rosa's work sheds light on long-standing conjectures related to the Plateau problem, which seeks to identify surfaces with least possible area among surfaces that span a prescribed boundary. An example is the positive answer obtained by De Rosa and his coauthors to the conjecture posed by the renowned mathematician William K. Allard in 1983 on the min-max construction of closed optimally regular anisotropic minimal surfaces in closed Riemannian manifolds. Anisotropic minimal surfaces minimize directionally dependent energy functionals, unlike isotropic minimal surfaces which minimize the area functional. These surfaces model natural phenomena where the surface tension varies with the orientation of the surfaces, such as crystalline structures and capillarity models.
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.
Antonio De Rosa has been awarded a European Research Council (ERC) grant to support his study of anisotropic geometric variational problems and this article is part of the results achieved within his ERC project ANGEVA.
