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Pubblicazioni scientifiche recenti

  • Arcozzi N., Citti G., Sarti A. Association fields of simple cells as parallel transport in a hyperbolic symplectic structure (preprint).
  • Avelina B., Capogna L., Citti G., Nyströmd K. Harnack estimates for degenerate parabolic equations modeled on the subelliptic p-Laplacian, Adv. in Math., v. 257, 1 June 2014, Pages 25–65
  • Barbieri, D. Citti G., Reproducing kernel Hilbert spaces of CR functions for the Euclidean Motion group. to appear on Analysis and Applications.
  • Barbieri D., Citti G., Cocci G., Sarti A., A cortical-inspired geometry for contour perception and motion integration. accepted on Journal of Mathematical Imaging and Vision
  • Capogna, L. Citti G. and Manfredini M., Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups, Analysis and Geometry in Metric Spaces 1, 2013- 255-275
  • Capogna L., Citti G. and Rea G., A subelliptic analogue of Aronson-Serrin’s Harnack Inequality. Math. Ann. 357 (2013), no. 3, 1175–1198.
  • Capogna L., Citti G. and Senni C., Sub -Riemannian heat kernels and mean curvature flows of graphs. J. Funct. Anal. 264 (2013), no. 8, 1899–1928.
  • G. Citti - M. Manfredini - A. Pinamonti - F. Serra Cassano Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group (2013) Calculus of Variations and Partial Differential Equations March 2014, Volume 49, Issue 3-4, pp 1279-1308
  • Citti G., Sarti A. Models of the Visual Cortex in Lie Groups, Advanced Courses in Mathematics, Springer, 2013.
  • Barbieri D. Citti G., Sarti A., An uncertainty principle underlying the functional architecture of V1. J Physiol Paris, 106(5-6):183-93(2012),
  • Citti G. Ferrari F., A sharp regularity result of solutions of a transmission problem, Proc. Amer. Math. Soc. 140 (2012) 615-620.
  • Citti G., Senni, C., Constant mean curvature graphs on exterior domains of the hyperbolic plane, Math. Zeit, (2012), no. 1-2, 531–550
  • Barbieri D., Citti G., Regularity of non charachteristic minimal graphs in Lie groups of step 2 and dimension 3, Journal des Mathématiques Pures et Appliquées 96(3):279-306, 2011.
  • Sarti A. Citti G., On the Origin and Nature of Neurogeometry La nuova critica 2011
  • Capogna L., Citti G., Manfredini M., Smoothness of lipschitz minimal intrinsic graphs in Heisenberg groups Hn, n > 1,J. Reine Angew. Math. 648 (2010), 75–110.
  • Citti, G., Manfredini, M., Sarti A., Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. Commun. Pure Appl. Anal. 9 (2010), no. 4, 905–927.
  • Capogna L., Citti G., Generalized mean curvature flow in Carnot groups, Comm. Partial Differential Equations 34 (2009), no. 7-9, 937–956 .
  • Capogna L., Citti G., Manfredini M., Regularity of non-characteristic minimal graphs in the Heisenberg group H1 Indiana Univ. Math. J. 58 (2009), no. 5, 2115–2160.
  • Sarti A., Citti G., Petitot J., The symplectic structure of the visual cortex, Biol Cybernetics.Volume 98, Number 1 / January, 2008, 33-48.
  • Citti G., Manfredini M., Implicit function theorem in Carnot-Carathèodory spaces Communication in Contemporary mathematics vol. 8, 5, 2006, 657-680.
  • Citti G., Manfredini M., Uniform Estimates of the fundamental solution for a family of Hypoelliptic operators, Potential Analysis, 25, (2006), 147-164.
  • Citti G., Sarti A., A cortical based model of perceptual completion in the Roto-Translation space, Journal of Mathematical Imaging and Vision, 2006, vol. 24, pp. 307 - 326
  • Citti G., Manfredini, M., ‘Blow-Up in Non-Homogeneous Lie Groups and rectifiability’, Houston Journal of Mathematics, Vol. 31, No. 2, 2005.
  • G.Citti, M.Manfredini e A. Sarti Neuronal oscillation in the visual cortex: Gamma-convergence to the Riemannian Mumford-Shah functional SIAM Jornal of Mathematical Analysis Volume 35, Number 6, 1394 - 1419.
  • G. Citti, M. Manfredini, A degenerate parabolic equation arising in image processing Communication on Applied Analysis, 8, 2004, 1, 125-141.
  • A. Sarti, G. Citti, M. Manfredini, From neural oscillations to variational problems in the visual cortex special issue of the Journal of Physiology, Volume 97, Issues 2-3, Pages 87-385 (2003).
  • G. Citti, M. Manfredini, Long time behavior of Riemannian mean curvature flow of graphs, Journal of Mathematical Analysis and Applications, 273 (2002), 353-369.
  • Sarti A., Citti G., Subjective surfaces and Riemannian mean curvature flow of graphs. Acta Math. Univ. Comenian. (N.S.) 70 (2000), no. 1, 85—103.
  • Equazione di Levi

  • G. Citti, G. Tomassini, Levi equation for almost complex structures Revista Matematica Iberoamericana, vol. 20, no. 1, 151-182.
  • G.Citti., E. Lanconelli e A. Montanari, Smoothness of Lipschitz continuous graphs, with non vanishing Levi curvature. (in collaborazione con ) Acta Math. 188 (2002), no. 1, 87--128.
  • G.Citti, A. Montanari, Regularity properties of solutions of a class of elliptic-parabolic nonlinear Levi type equations Trans. Amer. Math. Soc. 354 (2002), no. 7, 2819--2848
  • G.Citti., A. Montanari, Analytic estimates of solutions of the Levi equation J. Differential Equations 173 (2001), no. 2, 356--389.
  • G.Citti, Regularity of a solution of a nonlinear Hoermander type equation. Nonlinear Anal. 47 (2001), no. 1, 479--489.
  • G.Citti., A. Montanari, Strong solutions for the Levi curvature equation, Adv. Differential Equations, vol. 5,1-3 (2000), 323-342.
  • G.Citti., A. Montanari, $C^infty$ regularity of solutions of an equation of Levi's type in R2n+1 , Ann. Mat. Pura Appl. (4) 180 (2001), no. 1, 27--58.
  • On the smoothness of viscosity solutions of the prescribed Levi-curvature equation, (in collaborazione con E. Lanconel e A. Montanari )Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 10, 1999, 61-68.
  • Regularity properties of Levi flat graphs, (in collaborazione con A. Montanari ) C. R. Acad. Sci. Paris Sér. Math., 329, serie 1, 1999, 1049-1054.
  • $C^infty$ regularity of solutions of the Levi equation, Ann. Inst. H. Poincare, Anal. non Linéaire, 15, 4, 1998, 517-534.
  • $C^infty$ regularity of solutions of a quasilinear equation related to the Levi operator, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 23, 1996, 483-529.
  • A comparison theorem for the Levi equation, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 5, 3, 1993, 207-212.
  • Somme di quadrati di campi vettoriali

  • On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance (in collaborazione con A. Pascucci e S. Polidoro ) Diff. Int. Eq, 14 (2001), 701-738
  • Regularity properties of viscosity solutions of a non-H\"ormander degenerate equation (in collaborazione con A. Pascucci, S. Polidoro) J. Math. Pures Appl. (9) 80 (2001), no. 9, 901--918.
  • Hölder regularity of the solutions for operators which are sum of squares of vector fields plus a potential, (in collaborazione con G. Di Fazio ), Proc. Amer. Math. Soc., 122, 1994, 741-750.
  • Harnack's inequality for sum of squares of vector fields plus a potential, (con N. Garofalo, E. Lanconelli), Amer. J. Math., 115, 1993, 699-734.
  • Wiener Estimates at Boundary points for Hörmander operators, Boll Un. Mat. Ital. B(7), 1988, 667-681.
  • Punti critici di funzionali

  • Semilinear Dirichlet Problem Involving Critical Exponent for the Kohn Laplacian, Ann. Mat. Pura Appl. (4), 169, 1995, 375-392.
  • Critical semilinear equations on the Heisenberg group: the effect of the topology of the domain. (in collaborazione con F. Uguzzoni ) Nonlinear Anal., Theory Methods Appl. 46A, No.3, 399-417 (2001). .
  • Positive solutions of $\Delta_p u + u^{p-1} - q(x) u^\alpha = 0$in ${\mathbb{R} }^N$ NoDEA, Nonlinear Differ. Equ. Appl. 9, No.1, 1-14 (2002) (con F. Uguzzoni).


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