Manuel Ritoré got his Ph.D. degree in Mathematics at the University of Granada in 1997. Since then, his research interests have focused on geometric variational problems, with special attention to isoperimetric problems. In the last years, he became more interested in spaces with a more intricate structure, such as sub-Riemannian manifolds and more general metric measure spaces.
He made short post-doctoral research stays at MSRI-Berkeley and IMPA-Rio de Janeiro. Since 2004, he has been was awarded several MTM research grants as a principal investigator. He was a coordinator of the Spanish Network of Geometric Analysis and currently he is the local coordinator of the project GHAIA (Geometric and Harmonic Analysis with Industrial Applications) funded through the call H2020-MSCA-RISE-2017. He is also the founding Journal Editor of Analysis and Geometry in Metric Spaces, published by De Gruyter Open since 2013. Since 2007, he is a full professor at the Department of Geometry and Topology of the University of Granada.
Some remarkable results obtained alone or in collaboration are: complete classifications of isoperimetric sets in the 3-dimensional real projective space and in the product of a circle with Euclidean space; a complete classification of double bubbles in the 3-dimensional Euclidean space; a topological characterization of isoperimetric curves in convex surfaces; existence of solutions of the Allen-Cahn equation near non-degenerate minimal surfaces; an alternative proof of the isoperimetric conjecture for 3-dimensional Cartan-Hadamard manifolds; optimal isoperimetric inequalities outside convex sets, both in Euclidean space and in 3-dimensional Cartan-Hadamard manifolds; partial solutions to the isoperimetric conjecture in the sub-Riemannian Heisenberg groups; solutions of the Bernstein problem in the first Heisenberg group; regularity results for surfaces of prescribed mean curvature in 3-dimensional contact sub-Riemannian manifold; a Steiner’s formula in the Heisenberg groups; a Brunn-Minkowski inequality for metric measure spaces; and a characterization of isoperimetric regions of large volumes in Riemannian cylinders (product of a compact Riemannian manifold with Euclidean space).
He is currently interested in regularity problems for solutions of geometric variational problems in sub-Riemannian manifolds and spaces with low regularity, where classical approaches are useless, and also on applications of variational theory.