Francisco Martin

Some of my papers and preprints can be found bellow. Unfortunately, I do not have the pdf files of some of them (specially the old ones). However, if you are interested I can send you a hard copy.

The minimal surface on the left is a nonorientable minimal surface with helicoidal ends discovered by Leonor Ferrer and myself in 2005. It is a singly periodic surface and the quotient of the surface by the vertical translation is a twice punctured Klein bottle. If you are interested in more pictures, then click here

PAPERS AND PREPRINTS

• Uniqueness of semi graphical translators (with M. Saez and R. Tsiamis). Preprint arXiv2310.06980.
• Translating Annuli for Mean Curvature Flow  (with D. Hoffman and B. White). Advances in Mathematics, Volume 455, 2024, 109875. https://doi.org/10.1016/j.aim.2024.109875
• Annuloids and Delta-wings (with D. Hoffman and B. White). Advanced Nonlinear Studies, special issue in honor of Joel Spruck, 2024. https://doi.org/10.1515/ans-2023-0111
• Morse-Radó theory for minimal surfaces (with D. Hoffman and B.White). J. London Math. Soc., Vol. 108, Issue 4 (2023), 1669-1700.
• Finite entropy translating solitons in slabs (with E. S. Gama and N. M. Moller). Preprint arXIv:2209.01640 2022.
• Nguyen's Tridents and the Classification of Semigraphical Translators for Mean Curvature Flow  (with D. Hoffman and B. White). J. Reine Angew. Math., vol. 2022, no. 786, 2022, pp. 79-105 .
• Scherk-like Translators for Mean Curvature Flow. (with D. Hoffman and B. White). Journal of Differential Geometry, Volume 122 (3), 421-465, 2022.
• Notes on Translating Solitons of the Mean Curvature Flow (with D. Hoffman, T. Ilmanen and B. White). Minimal surfaces: integrable systems and visualisation, 147–168, Springer Proc. Math. Stat., 349, Springer, Cham, [2021], ©2021.
• Families of minimal surfaces in H²xR foliated by arcs and their Jacobi fields (with L. Ferrer, R. Mazzeo and M. Rodriguez). Minimal surfaces: integrable systems and visualisation, 67–88, Springer Proc. Math. Stat., 349, Springer, Cham, [2021], ©2021.
• The Jenkins-Serrin problem for horizontal translating graphs in M x R (width E. S. Gama,  E. Heinonen and J. Lira). Rev. Mat. Iberoam, Volume 37, Issue 3, 2021, pp. 1083–1114. DOI: 10.4171/rmi/1221
• Translating solitons of the mean curvature flow asymptotic to hyperplanes in Rⁿ⁺¹ (with Eddygledson S. Gama). International Mathematics Research Notices, Volume 2020, Issue 24, December 2020, Pages 10114–10153, https://doi.org/10.1093/imrn/rny278
• Graphical Translators for Mean Curvature Flow  (with D. Hoffman, T. Ilmanen and B. White). Calculus of Variations and PDE’s, vol. 58, (2019), art. 117.
• Translating solitons in Riemannian products (with J. H. de Lira). Journal of Differential Equations Volume 266, Issue 12, 5 June 2019, Pages 7780-7812.
• A characterization the of the grim reaper cylinder (with J. Perez-Garcia, A. Savas-Halilaj and K. Smoczyk). Journal für reine und angewandte Mathematik, Volume 2019, Issue 746 (Jan 2019), pp. 209–234.
• Properly embedded minimal annuli in H^2xR (with L. Ferrer, R. Mazzeo and M. Rodriguez). Math. Ann., Volume 375, Issue 1–2, (2019), pp 541–594.
• On the topology of translating solitons of the mean curvature flow (with A. Savas-Halilaj and K. Smoczyk). Calculus of Variations and PDE’s, Volume 54, Issue 3 (2015) 2853 — 2882. http://link.springer.com/article/10.1007/s00526-015-0886-2
• A construction of a complete bounded null curve in C^3 (with L. Ferrer, M. Umehara and K. Yamada)  Kodai Math. J. 2014 (vol 37) pages 59-96.
• Properly embedded, area-minimizing surfaces in hyperbolic 3-space (with Brian White). Journal of Differential Geometry 97 (3) (2014), 515-544.
• Minimal surfaces with positive genus and finite total curvature in H^2xR (with Rafe Mazzeo and Magdalena Rodríguez). Geometry and Topology 18 (2014) 141–177. arXiv:1208.5253. 
• Non simply connected minimal planar domains in H^2xR (with Magdalena Rodriguez). Transactions of the A.M.S. 365 (2013), 6167-6183. 
• Existence of proper minimal surfaces of arbitrary topological type (with L. Ferrer y W. H. Meeks III). Advances in Mathematics Volume 231, Issue 1,  (2012) 378–413. http://arxiv.org/abs/0903.4194.
• Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded (with M. Umehara and K. Yamada). Rev. Mat. Iberoam. Volume 30, Issue 1, 2014, pp. 309–316 DOI: 10.4171/RMI/779.
•  Calabi-Yau domains in three manifolds (with W. H. Meeks III). American J. of Math. Volume 134, Number 5 (2012), 1329-1344.
• Complete bounded holomorphic curves immersed in C^2 with arbitrary genus (with M.Umehara and K. Yamada).  Proc. A.M.S. 137 (2009), 3437-3450.
• Density theorems and applications. Proceedings of the workshop "Progress in surface theory". Oberwolfach April 29th - May 5th, 2007. 
• Complete bounded null curves immersed in C3 and SL(2,C) (with M. Umehara and K. Yamada). Calculus of Variations and P.D.E.'s (2009) 36:119-139 DOI10.1007/s00526-009-0226-5.
• Density theorems for complete minimal surfaces in R3 (with A. Alarcon and L. Ferrer). GAFA. 18 (2008), 1-49.
• A Jordan curve spanned by a complete minimal surface (with N. Nadirashvili). Arch. Ration. Mech. Anal. 184(2) (2007), 285-301. 
• Bounded domains which are universal for minimal surfaces (with W. H. Meeks III and N. Nadirashvili). American J. of Math. 129(2) (2007), 455-461.
• A uniqueness theorem for the singly periodic genus-one helicoid (with A. Alarcón and L.Ferrer). Trans. A.M.S. 359(6) (2007), 2819-2829.
• The embedded singly periodic Scherk-Costa surfaces (with V. Ramos-Batista). Math. Ann. 336(1) (2006), 155-189. 
• Complete proper minimal surfaces in convex bodies of R3 (II) (with S. Morales). Comm. Math. Helv. 81(3) (2006), 699-725.
• Complete nonorientable minimal surfaces in a ball (with F.J. López and Santiago Morales). Trans. Amer. Math. Soc. 358 (2006), 3807-3820.  
• Minimal surfaces with helicoidal ends (with L. Ferrer).  Math. Zeit. 250(4) (2005), 807-839. 
• Complete proper minimal surfaces in convex bodies (with S. Morales). Duke Math. J. 128(3) (2005), 559-593.
• On the asymptotic behavior of a complete bounded minimal surface in R^3 (with S. Morales).  Trans. A.M.S. 356(10) (2004), 3985-3994. 
• Properly embedded minimal disks bounded by non compact polygonal lines (with L. Ferrer). Pacific J. Math., 214(1) (2004), 55-88. 
• Adding handles to Nadirashvili's surfaces  (with F. J. López y S. Morales). Journal of  Differential Geometry 60 (2002), no. 1, 155-175.
• Minimal surfaces in a wedge of a slab (with F. J. López). Communications in Analysis and Geometry, Vol. 9, n. 4 (2001), 683-723.
• A complete bounded minimal cylinder in R^3 (with S. Morales). Michigan Math. J. Vol. 47 (2000), n. 3, 499-514. 
• Properly Embedded Minimal Surfaces with Three Ends (with M. Weber). Duke Math. J. Volume 107, Number 3, (2001) 533-560. 
• A note on the Gauss map of a complete nonorientable minimal surface (with F.J. López).  Pacific J. Math., Vol. 194, No. 1, (2000) 129-135.  
• Uniqueness of properly embedded minimal surfaces bounded by straight lines (with F.J. López). J. Australian Math. Soc. Series A 69 (2000), no. 3, 362-402.
• A survey on complete minimal surfaces in R ^3. Publicacions Matematiques, Vol. 43, No. 2, (1999) 341-449. (with F J López).
• Complete minimal surfaces derived from Chen-Gackstätter genus two example. Pacific J. Math., Vol. 184, No. 2, (1998) 311-332. (with F.J. Lopez and D. Rodríguez). 
• A new approach to the construction of complete minimal surfaces derived from the genus two Chen-Gackstatter example. Illinois J. Math., Vol. 41, No. 2, (1997) 171-192; (with D. Rodríguez). 
• A characterization of the periodic Callahan-Hoffman-Meeks surfaces in terms of their symmetries. (with D. Rodríguez) Duke Math. J., Vol. 89, No. 3, (1997) 445-463. 
• A note on the uniqueness of the periodic Callahan-Hoffman-Meeks surfaces. Geometriae Dedicata 86 (2001), no. 1-3, 185-190.
• Complete nonorientable minimal surfaces with the highest symmetry group. American J. Math., Vol. 119, No. 1, (1997) 55-81; (with F. J. López). 
• Complete nonorientable minimal surfaces and symmetries. Duke Math. J., Vol. 79, No. 3, (1995) 667-686; (with F. J. López).