Francisco Martín is a mathematician from Granada and a full professor in the Department of Geometry and Topology at the University of Granada (UGR). His career combines a strong commitment to teaching with an important research output in the field of differential geometry, particularly in the study of minimal surfaces and geometric flows in three-dimensional manifolds.
F. Martín has devoted his research to fundamental problems related to the geometry of surfaces in spaces such as ℝ³, ℍ² × ℝ, and ℍ³. His main interests include complete and embedded minimal surfaces, translating solitons of the mean curvature flow, the Calabi-Yau conjecture, and problems involving constant mean curvature surfaces.
Over the course of his career, he has published more than 60 scientific articles in internationally recognized journals. Among his most influential contributions are:
- The construction of new classes of complete and embedded minimal surfaces in ℝ³, many of which exhibit interesting symmetries or nontrivial asymptotic behavior.
- Significant results on complete graphical solutions to the minimal surface equation in product manifolds such as ℍ² × ℝ.
- Deep studies on the stability and classification of solitons of the mean curvature flow in various geometric contexts.
His work has appeared in top-tier journals, including:
- Duke Mathematical Journal
- Advances in Mathematics
- American Journal of Mathematics
- Transactions of the American Mathematical Society
- Journal of Differential Geometry
- Journal of Differential Equations
- Mathematische Annalen
- Calculus of Variations and Partial Differential Equations
He has collaborated with well-known mathematicians such as David Hoffman, Tom Ilmanen, Rafe Mazzeo, William H. Meeks, Nikolai Nadirashvili and Brian White, among others. These collaborations have led to significant advances in understanding the global properties of immersed surfaces and their interaction with the ambient geometry.
In addition to his research, F. Martín is actively involved in training new generations of mathematicians. He has supervised 6 PhD theses and has led research projects funded by the Spanish Ministry of Science and Innovation and the Andalusian Regional Government. F. Martín is currently co-responsible (jointly with Miguel Sanchez) of the research project, entitled "Semi-Riemannian Geometry and Geometric Flows in Mathematical Physics”, funded by the Spanish Ministery of Science and Innovation (MICINN).
He is also leading the project "Differential Equations in Manifolds, Mathematical Physics and Applications" that is financed by Junta de Andalucia and the UE, through the ERDEF program. This project brought together researchers from Cordoba, Malaga and Granada to work on the study of evolution equations in Riemannian and Semi-Riemannian Geometry: combining the expertise of the network partners in the areas of relativity, Finsler geometry, geometric flows, minimal surfaces and integrable systems which allowed new approaches in this research area.
From 2016 to 2020, Martín was responsible in Granada of the International Network Grant Minimal surfaces: Integrable systems and visualisation, a joint research project of the Universities of Leicester (UK), Tsukuba (Japan), U.C. Cork (Ireland), T.U. München (Germany), funded by the Leverhulme Trust (UK) starting on September1, 2016. The coordinator of this grant was Prof. Katrin Leschke (Leicester).
If you want to see Martín's research profile in Scopus, Google Scholar and ZB, you can click below
http://orcid.org/0000-0001-8380-0465
https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=367890
https://zbmath.org/authors/?q=ai:martin.francisco
https://www.scopus.com/authid/detail.uri?authorId=35254096700
https://scholar.google.es/citations?user=MMsjxzsAAAAJ
https://www.researchgate.net/profile/Francisco_Martin8
