Graham Smith PhD HDR

Instituto de Matemática
UFRJ, Av. Athos da Silveira Ramos 149,
Centro de Tecnologia - Bloco C,
Cidade Universitária - Ilha do Fundão,
Caixa Postal 68530, 21941-909,
Rio de Janeiro, RJ - BRASIL

+55 21 9 79 70 10 01

My address may be found in my CV (see below).


Research Interests

I am a classical differential geometer. My work largely concerns the classical theory of submanifolds and its manifestations in contemporary mathematics. These may be found in hyperbolic geometry, Teichmüller theory, general relativity, integrable systems theory, differential topology, the theory of curvature flows, and the theory of totally non-linear partial differential equations.

Key Words: hypersurfaces, fundamental forms, curvature, moduli, singularities, totally non-linear PDEs, hypoelliptic regularity, differential topology



Ensino (Teaching)

  1. 2020/1 - MAC745 - Geometria Diferencial (Mestrado)
  2. 2020/4 (PLE) - MAC855 - Geometria Riemanniana (Doutorado)
  3. 2021/1 - MAC745 - Geometria Diferencial (Mestrado)
  4. 2021/1 - MAC857 - Análise Geométrica (Doutorado)
  5. 2021/1 - MAC248 - Cálculo IV (Métodos Matemáticos), Aulas síncronas, Aulas assíncronas




The Pangolin seminar takes place every other Tuesday online in Zoom.

For more information, please consult our webpage.



Habilitation à diriger des recherches (HDR)

Defended 8th February 2017, Université Grenoble-Alpes

The French "Habilitation à diriger des recherches", introduced in 1984, replaced the older "Doctorat d'État" and is roughly equivalent to the British D.Sc. It is the general requirement for applying for a French "Professeur" position as well as for supervising PhD students within the French system.




Defended 13th December 2004, Université Paris-Sud, Orsay




Last Updated 23rd September 2022.

Published in Peer Reviewed Journals

  1. On complete embedded translating solitons of the mean curvature flow that are of finite genus, to appear in Analysis and PDE
  2. On eternal mean curvature flows of tori in perturbations of the unit sphere (joint with Claudia Magaño), to appear in Pacific J. Math.
  3. Möbius structures, hyperbolic ends and k-surfaces in hyperbolic space, to appear in "In the Tradition of Thurston, Vol. II", (Ohshika K., Papadopoulos A. ed.), Springer Verlag, (2022)
  4. On the Morse index of higher-dimensional free boundary minimal catenoids (joint with Ari Stern, Hung Tran and Detang Zhou), to appear in Calc. Var. PDEs.
  5. Prescription de courbure des feuilles des laminations: retour sur un théorème de Candel (joint with Sébastien Alvarez), to appear in Ann. Inst. Fourier
  6. On the Weyl problem in Minkowski space, Int. Math. Res. Not., (2021)
  7. On the elliptic sinh-Gordon equation with Durham boundary conditions (joint with Martin Kilian), Nonlinearity, 34, no. 8, 5119--5135 (also available in French)
  8. On an Enneper-Weierstrass-type representation of constant Gaussian curvature surfaces in 3-dimensional hyperbolic space, in "Minimal surfaces: Integrable systems and Visualisation" (Hoffmann T., Kilian M., Leschke K., Martin G. ed.), Springer Proceedings in Mathematics and Statistics, 349, (2021)
  9. Earthquakes and graftings of hyperbolic surface laminations (joint with Sébastien Alvarez), Int. Math. Res. Not., (2020)
  10. A short proof of an assertion of Thurston concerning convex hulls, in "In the tradition of Thurston" (Alberge V., Ohshika K., Papadopoulos A. ed.), Springer Verlag, (2020)
  11. The Plateau problem for convex curvature functions, Ann. Inst. Fourier, 70, no. 1, 1--66, (2020)
  12. A note on invariant constant curvature immersions in Minkowski space (joint with François Fillastre), Geom. Dedicata, 206, no. 1, 75--82, (2020)
  13. Degree Theory of Immersed Hypersurfaces (joint with Harold Rosenberg), Mem. Amer. Math. Soc., 265, no. 1290, (2020)
  14. Eternal forced mean curvature flows II - Existence, Pacific J. Math., 299, no. 1, 191--235, (2019)
  15. The Morse index of the critical catenoid (joint with Detang Zhou), Geom. Dedicata, 201, 13--19, (2019)
  16. Group actions and scattering problems in Teichmueller theory (joint with François Fillastre), in The Handbook of Group Actions, Vol. III, Advanced Lectures in Mathematics, 40, International Press, Boston, (2018)
  17. Constant scalar curvature hypersurfaces in (3+1)-dimensional GHMC Minkowski spacetimes, J. Geometry Phys., 128, 99--117, (2018)
  18. Free boundary minimal annuli in convex three-manifolds (joint with Davi Máximo and Ivaldo Nunes), J. Diff. Geom., 106, No. 1, (2017)
  19. Bifurcation of solutions to the Allen-Cahn equation, J. London Math. Soc., 94, no. 3, (2016), 667-687
  20. Global Singularity Theory for the Gauss Curvature Equation (book), Ensaios Matemáticos, 28, (2015), 1-114
  21. Eternal forced mean curvature flows I - a compactness result, Geom. Dedicata, 176, no. 1, (2015), 11-29
  22. Hyperbolic Plateau problems, Geom. Dedicata, 176, no. 1, (2015), 31-44
  23. Compactness results for immersions of prescribed Gaussian curvature II - geometric aspects, Geom. Dedicata, 172, no. 1, (2014), 303-350
  24. The Perron Method and the Non-Linear Plateau problem Geom. Dedicata, 163, no. 1, (2013), 159-165, (joint with Andrew Clarke)
  25. The non-linear Plateau problem in non-positively curved manifolds, Trans. Amer. Math. Soc., 365, (2013), 1109-1124
  26. Special Lagrangian curvature, Math. Annalen, 355, no. 1, (2013), 57-95
  27. Compactness results for immersions of prescribed Gaussian curvature I - analytic aspects, Adv. Math., 229, (2012), 731-769
  28. Moduli of Flat Conformal Structures of Hyperbolic Type, Geom. Dedicata, 154, no. 1, (2011), 47-80
  29. Equivariant Plateau problems, Geom. Dedicata, 140, no. 1, (2009), 95-135
  30. An Arzela-Ascoli Theorem for Immersed Submanifolds, Ann. Fac. Sci. Toulouse Math., 16, no. 4, (2007), 817-866
  31. Problèmes de Plateau equivariants, Sémin. Théor. Spectr. Géom., 24, (2007), 67-78
  32. Pointed k-surfaces, Bull. Soc. Math. France, 134, no. 4, (2006), 509-557

Papers Submitted for Review

  1. improved! On the asymptotic Plateau problem in Cartan-Hadamard manifolds
  2. On the asymptotic geometry of finite-type k-surfaces in three-dimensional hyperbolic space
  3. On embedded minimal surfaces of Costa-Hoffman-Meeks type in hyperbolic space (joint with Asun Jiménez Grande)

Completed Papers awaiting Revision prior to Resubmission

Despite being satisfied with the results of these papers, I am convinced that their presentation could be greatly improved, and I therefore aim to revise them as the time presents itself.

  1. Eternal forced mean curvature flows III - Morse homology
  2. Constant curvature hyperspheres and the Euler Characteristic


  1. The non-linear Dirichlet problem in Hadamard manifolds
  2. Finite area and volume of pointed k-surfaces
  3. A Brief Note on Foliations of Constant Gaussian Curvature
  4. A Brief Note on Special Lagrangian Submanifolds in Euclidean Space
  5. An Origami Dog - pdf ps

Selected Talks

  1. Origami: arte, matemática e tecnologia (slides available here)
  2. On the Weyl problem in Minkowski space (slides available here)
  3. The Kulkarni-Pinkall form and locally strictly convex immersions in H^3 (slides available here)
  4. On eternal forced mean curvature flows of tori in perturbations of the unit sphere (slides available here)
  5. On the asymptotic structure of finite-type k-surfaces in 3-dimensional hyperbolic space (slides available here)
  6. Vida e ciência: o ponto de vista de um matemático. slideshow aqui e texto aqui
  7. Milking the cow: getting the most out of functional norms
  8. Constant mean curvature annuli and the sinh-Gordon equation
  9. Complete embedded minimal surfaces of Costa-Hoffman-Meeks type in 3-dimensional hyperbolic space
  10. On the Morse Index of higher-dimensional free boundary minimal catenoids (Niterói, 14th March 2018), (Maceió, 23rd March 2018)
  11. Constant scalar curvature time functions over GHMC Minkowski spacetimes
  12. Morse homology and problems of prescribed mean curvature
  13. On singular perturbations of the Morse complex (slides available here)
  14. On translating solitons for the mean curvature flow that are of finite genus (Maceio, 17th March 2015), (Granada, 9th April 2015)
  15. Perturbing the Costa Surface
  16. An Enneper-Weierstrass type representation for constant extrinsic curvature surfaces in hyperbolic space
  17. Free-boundary minimal annuli in convex 3-manifolds

Mathematical fragments

Including pleasing observations and simple proofs of well-known results that may be of interest to others.

  1. On groups of diffeomorphisms of Hölder type.
  2. A result of Thurston concerning pleated surfaces.
  3. On the Hausdorff property of the Cheeger-Gromov topology.
  4. On the Rauch and Topogonov comparison theorems.



Research Statement and Curriculum Vitae

Important - My email address may be found in my CV. The addresses in these files have however been censored to protect against spam. To obtain my address, simply replace "g*a*a*a*d*e*s*i*h" with "grahamandrewsmith".

An up-to-date CV is also maintained on the website of the Brazilian Scientific Research Council (CNPq).



Art and Mathematics - Interesting Links

  • A beleza escondida da matemática
  • A charming online exhibition produced by the Museu do Amanhã for which I provided scientific consultancy.

  • Symmetry in Moorish and Other Ornaments
  • Moorish tilings in the Alhambra (Granada, Spain) have symmetry groups belonging to 13 of the 17 different chrystalographic classes. The remaining 4 groups were later identified in the adjoining museum.

  • Selected origami artists
  • Eric Joisel

    Jean Claude Correia

    Paul Jackson

    Robert J. Lang

    Vincent Floderer

  • Blooms
  • Animated sculptures by John Edmark.

  • Strandbeest
  • Geometry comes to life with Theo Jansen's eolian creatures.

  • The Wintergatan marble machine
  • Technically more basic engineering than mathematics, but still impressive.



    Good Reads

  • The miracle of Purun Baghat, by Rudyard Kipling
  • When did the mundane become sacred? It happened before our very eyes, and we never even noticed.

  • The Gulag Archipelago, Parts I-II, Parts III-IV, Parts V-VII, Aleksandr Solzhenitsyn
  • Last and first men, by Olaf Stapledon
  • Harrison Bergeron, by Kurt Vonnegut
  • We, by Eugene Zamiatin
  • The Portrait, by Nikolai Gogol


    Spring School



    Russian Roulette

      click                       click
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      Graham Smith, Graham Andrew Smith, Mathematics, curvature, compactness, geometry, topology, analysis, geometric analysis, differential geometry, differential topology, Degree theory, Morse, Morse theory, Floer, Floer homology, Plateau, Plateau problems, Minkowski, Minkowski problems, mean curvature, extrinsic curvature, special Lagrangian curvature, geotop