Minimal surfaces
Complete and embedded surfaces, topology, asymptotic geometry and Calabi–Yau type questions.
Differential Geometry · Geometric Analysis
Geometry in motion.
I am a Full Professor in the Department of Geometry and Topology at the University of Granada. My research is centered on minimal surfaces, geometric flows, translating solitons, and nonlinear geometric PDEs.
Francisco Martín
University of Granada
“
Di contr'a Pietro vedi sedere AnnaDante Alighieri · Divina Comedia, Canto XXXII
tanto contenta di mirar sua figlia,
che non move occhio per cantare osanna;
Research
Surfaces, flows, and the geometry behind them.
My work concerns the global geometry of surfaces in spaces such as ℝ³, ℍ² × ℝ and ℍ³, with particular emphasis on complete and embedded minimal surfaces, solitons for mean curvature flow, and geometric PDEs in Riemannian and Lorentzian settings.
Mean curvature flow
Singularities, tangent flows, topology change, shrinkers and expanders.
Translating solitons
Classification, entropy, semigraphical examples, annuloids and related geometric PDEs.
Geometric analysis
Variational methods, nonlinear PDEs, Lorentzian geometry, and global questions for geometric surfaces.
Selected recent work
Latest papers & preprints.
2026
Minimal surfaces with rapid area growth
with Tobias H. Colding and William P. Minicozzi II
2026
Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture
with David Hoffman and Brian White
2025
Uniqueness of tangent planes and (non-)removable singularities at infinity for collapsed translators
with Eddygledson S. Gama and Niels Martin Møller
2025
Generating Shrinkers by Mean Curvature Flow
with David Hoffman and Brian White
2024
Finite entropy translating solitons in slabs
with Eddygledson S. Gama and Niels Martin Møller
2024
Complete translating solitons in Lorentzian Geometry
with Leonor Ferrer and Miguel Sánchez
2024
Classification of semigraphical translators
with Mariel Sáez, Raphael Tsiamis and Brian White
Work in progress
Current projects.
Collapsed translating solitons with planar wings
With Eddygledson S. Gama and Niels Martin Møller.
Finite total extrinsic curvature in ℍ² × ℝ
With Brian Firester, Rafe Mazzeo and Raphael Tsiamis.
Classification of algebraic translators
With Eddygledson S. Gama and Niels Martin Møller.
Geometry gallery
Some surfaces are best seen.
Weak solutions for Geometric Evolution Equations and Variational Problems
BIRS–Granada · Granada, Spain
Mathematics Colloquium
Monash University · Melbourne, Australia
H-Workshop
Granada, Spain
Analysis Seminar
Sapienza University of Rome · Rome, Italy
IV Coloquio de Geometría y Topología Granada–Málaga
Granada, Spain
Workshop on Geometry and PDEs
University of Copenhagen
Contact
University of Granada.
Department of Geometry & Topology · Faculty of Sciences.
Email
fmartin@ugr.es
Phone
+34 958 242 079
Address
Departamento de Geometría y Topología
Campus de Fuentenueva, s/n
18071 Granada, Spain
UGR profile
Official profile ↗