Professor Ros is Professor of Geometry and Topology at the University of Granada. He is among the best-reputed experts in minimal surface theory, although his contributions have been fundamental to a much wider field, namely Geometrical Analysis. With more than 70 publications in reference journals, his fields of specialization are diverse, from geometry of Riemannian manifolds, minimal surfaces, isoperimetric-type problems, variational methods, etc.
As examples of his most outstanding scientific contributions, we can mention the classification of compact Kaehler manifolds with positive holomorphic sectional curvature (Annals of Mathematics 1985), the solution of the "double bubble conjecture" in relation to the isoperimetric problem (Annals of Mathematics 2002), the classification of properly embedded minimal planar domains (Annals of Mathematics 2015), the best solution to date to the Hoffman-Meeks conjecture for embedded minimal surfaces (Acta Mathematica 2019) and the classification of constant mean curvature spheres in homogeneous manifolds of dimension three (Inventiones Mathematicae 2020). In addition, he has given conferences in the most prestigious forums such as the ICM in Madrid 2006.
It stands out his interest in deep geometry problems, some proposed by Fields medalists as S.T. Yau. In these problems, Ros has contributed original techniques that relate geometry and PDE, among which we mention the following ones:
-His integral approach to the characterization of the n-dimensional sphere as the only compact embedded hypersurface with constant scalar curvature in Euclidean space.
-The so-called "Lopez-Ros deformation", which has been crucial to classify complete embedded minimal surfaces with total finite curvature in Euclidean three-space, and in relation to producing counterexamples to the Calabi-Yau problem.
-His groundbreaking connection of the isoperimetric problem with Crystallography (Journal AMS 2004) capturing the interest of scientists from Materials Science, Nanotechnology, and other fields.
-His studies on Willmore surfaces in relation to the group of conformal transformations of the three-sphere were fundamental for the solution by Marques and Neves of the Willmore conjecture.
Especially remarkable is the powerful school of geometry of the University of Granada, which has evolved over three decades around Professor Ros. Formed by several generations of internationally recognized researchers, it has made Granada a reference point in minimal and constant mean curvature surfaces.
He is currently a member of the Editorial Board of "Revista Matemática Iberoamericana" (European Mathematical Society).