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).


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 Anglo-American 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



Research Interests

Geometric analysis, differential topology, Morse/Floer theory, Teichmüller theory

Key Words: embeddings and immersions, curvature problems, elliptic and parabolic PDEs, degree theory, Morse/Floer theory




Last Updated 11th September 2020.

Published in Peer Reviewed Journals

  1. Earthquakes and graftings of hyperbolic surface laminations (joint with Sébastien Alvarez), to appear in Int. Math. Res. Not.
  2. On an Enneper-Weierstrass-type representation of constant Gaussian curvature surfaces in 3-dimensional hyperbolic space, to appear in "Minimal surfaces: Integrable systems and Visualisation", Springer Proceedings in Mathematics
  3. The Plateau problem for convex curvature functions, Ann. Inst. Fourier, 70, no. 1, 1--66, (2020)
  4. A note on invariant constant curvature immersions in Minkowski space (joint with François Fillastre), Geom. Dedicata, 206, no. 1, 75--82, (2020)
  5. A short proof of an assertion of Thurston concerning convex hulls, to appear in "In the tradition of Thurston" (Alberge V., Ohshika K., Papadopoulos A. ed.), Springer Verlag, (2020)
  6. Degree Theory of Immersed Hypersurfaces (joint with Harold Rosenberg), Mem. Amer. Math. Soc., 265, no. 1290, (2020)
  7. Eternal forced mean curvature flows II - Existence, Pacific J. Math., 299, no. 1, 191--235, (2019)
  8. The Morse index of the critical catenoid (joint with Detang Zhou), Geom. Dedicata, 201, 13--19, (2019)
  9. 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)
  10. Constant scalar curvature hypersurfaces in (3+1)-dimensional GHMC Minkowski spacetimes, J. Geometry Phys., 128, 99--117, (2018)
  11. Free boundary minimal annuli in convex three-manifolds (joint with Davi Máximo and Ivaldo Nunes), J. Diff. Geom., 106, No. 1, (2017)
  12. Bifurcation of solutions to the Allen-Cahn equation, J. London Math. Soc., 94, no. 3, (2016), 667-687
  13. Global Singularity Theory for the Gauss Curvature Equation (book), Ensaios Matemáticos, 28, (2015), 1-114
  14. Eternal forced mean curvature flows I - a compactness result, Geom. Dedicata, 176, no. 1, (2014), 11-29
  15. Hyperbolic Plateau problems, Geom. Dedicata, 176, no. 1, (2014), 31-44
  16. Compactness results for immersions of prescribed Gaussian curvature II - geometric aspects, Geom. Dedicata, 172, no. 1, (2014), 303-350
  17. The Perron Method and the Non-Linear Plateau problem Geom. Dedicata, 163, no. 1, (2013), 159-165, (joint with Andrew Clarke)
  18. The non-linear Plateau problem in non-positively curved manifolds, Trans. Amer. Math. Soc., 365, (2013), 1109-1124
  19. Special Lagrangian curvature, Math. Annalen, 335, no. 1, (2013), 57-95
  20. Compactness results for immersions of prescribed Gaussian curvature I - analytic aspects, Adv. Math., 229, (2012), 731-769
  21. Moduli of Flat Conformal Structures of Hyperbolic Type, Geom. Dedicata, 154, no. 1, (2011), 47-80
  22. Equivariant Plateau problems, Geom. Dedicata, 140, no. 1, (2009), 95-135
  23. An Arzela-Ascoli Theorem for Immersed Submanifolds, Ann. Fac. Sci. Toulouse Math., 16, no. 4, (2007), 817-866
  24. Pointed k-surfaces, Bull. Soc. Math. France, 134, no. 4, (2006), 509-557

Papers Submitted for Review

  1. new! Prescription de courbure des feuilles des laminations: retour sur un théorème de Candel (joint with Sébastien Alvarez)
  2. new! On the Weyl problem in Minkowski space
  3. new! On eternal mean curvature flows of tori in perturbations of the unit sphere (joint with Claudia Magaño)
  4. improved! On the elliptic sinh-Gordon equation with Durham boundary conditions (joint with Martin Kilian, also in French)
  5. On the asymptotic geometry of finite-type k-surfaces in three-dimensional hyperbolic space
  6. On embedded minimal surfaces of Costa-Hoffman-Meeks type in hyperbolic space (joint with Asun Jiménez Grande)
  7. On the Morse index of higher-dimensional free boundary minimal catenoids (joint with Ari Stern, Hung Tran and Detang Zhou)
  8. Eternal forced mean curvature flows III - Morse homology
  9. On complete embedded translating solitons of the mean curvature flow that are of finite genus

    Note: The above paper was submitted for review to Communications in Analysis and Geometry on the 2nd of May 2015. After 30 months, despite repeated requests, I had still received no conclusive review or editorial decision. The paper has since been withdrawn. My complete correspondence with this journal can be found here.

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. Constant curvature hyperspheres and the Euler Characteristic
  2. The non-linear Dirichlet problem in Hadamard manifolds

Conference Proceedings

  1. Problèmes de Plateau equivariants Actes de Séminaire de Théorie Spectrale et Géométrie. Vol. 24. Année 2005--2006, 67-78, Sémin. Théor. Spectr. Géom., 24, Univ. Grenoble I, Saint-Martin-d'Hères, 2007.


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

Selected Talks

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



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".

Both CVs are now very old.



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.

  • Origami
  • Work by Robert J. Lang.

  • More origami
  • Work by Eric Joisel.

  • 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


    Spring School



    Russian Roulette

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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