Preprints

  1. V. Magnani and D. Tiberio. On the Michor-Mumford phenomenon in the infinite dimensional Heisenberg group

  2. G. M. Leccese and V. Magnani. A study of measure-theoretic area formulas

  3. V. Magnani. Rotational symmetries and spherical measure in homogeneous groups

  4. F. Corni and V. Magnani. Area formula for regular submanifolds of low codimension in Heisenberg groups


Papers

  1. V. Magnani and A. Minne. Optimal Regularity of Solutions to No-Sign Obstacle-Type Problems for the Sub-Laplacian
    Anal. PDE, to appear (postprint available)

  2. K. O. Idu, V. Magnani, F. P. Maiale. Characterizations of k-rectifiability in homogenous groups
    J. Math. Anal. Appl. 500, n.2, 125120, 20 pp., (2021) (postprint available)

  3. V. Magnani and D. Tiberio. A remark on vanishing geodesic distances in infinite dimensions
    Proc. Amer. Math. Soc., vol. 148, n.8, 3653-3656, (2020) (postprint available)

  4. V. Chousionis, V. Magnani and J.T. Tyson. On uniform measures in the Heisenberg group
    Adv. Math., vol. 363, 106980, 42 p., (2020) (postprint available)

  5. G.E. Comi and V. Magnani. The Gauss-Green theorem in stratified groups
    Adv. Math., vol. 360, 106916, 85 p., (2020) (postprint available)

  6. V. Magnani, A. Pinamonti and G. Speight. Porosity and Differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups
    Ann. Mat. Pura Appl. (4), vol. 199, n.3, 1197-1220, (2020) (postprint available)

  7. V. Magnani. Towards a theory of area in homogeneous groups
    Calc. Var. Partial Differential Equations, vol. 58, n.3, Art. 91, 39 pp., (2019)

  8. V. Magnani and D. Trevisan. On Lipschitz vector fields and the Cauchy problem in homogeneous groups
    Commun. Contemp. Math., vol. 20, n.5, 1750057, 21 pp., (2018)

  9. V. Magnani, D. Trevisan and E. Stepanov. A rough calculus approach to level sets in the Heisenberg group
    J. Lond. Math. Soc., vol. 97, n.3, 495-522, (2018)

  10. V. Magnani. Some remarks on densities in the Heisenberg group
    Ann. Acad. Sci. Fenn. Math. vol. 42, n.1, 357-365, (2017)

  11. V. Magnani and A. Zapadinskaya. A Gromov's dimension comparison estimate for rectifiable sets
    Selecta Math. (N.S.), vol. 23, n.2, 1153-1174, (2017)

  12. V. Magnani. A new differentiation, shape of the unit ball and perimeter measure
    Indiana Univ. Math. J., vol. 66, n.1, 183-204, (2017)

  13. V. Magnani and M. Scienza. Regularity estimates for convex functions in Carnot-Carathéodory spaces
    Rev. Mat. Iberoam., vol. 32, n.3, 835-858, (2016)

  14. V. Chousionis, V. Magnani, J. T. Tyson. Removable sets for Lipschitz harmonic functions on Carnot groups
    Calc. Var. Partial Differential Equations, vol. 53, n.3-4, 755-780, (2015)

  15. V. Magnani. On a measure-theoretic area formula
    Proc. Roy. Soc. Edinburgh Sect. A, vol. 145, 885-891, (2015)

  16. V. Magnani, J. Malý and S. Mongodi. A low rank property and nonexistence of higher dimensional horizontal Sobolev sets
    J. Geom. Anal., vol. 25, n.3, 1444-1458, (2015)

  17. L. Ambrosio, R. Ghezzi and V. Magnani. BV functions and sets of finite perimeters in sub-Riemannian manifolds
    Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 32, n.3, 489-517, (2015)

  18. V. Magnani, J. T. Tyson and D. Vittone. On transversal submanifolds and their measure
    J. Anal. Math., vol. 125, 319-351, (2015)

  19. V. Magnani and T. Rajala. Radon-Nikodym property and area formula for Banach homogeneous group targets
    Int. Math. Res. Not., n.23, 6399-6430, (2014)

  20. V. Magnani and M. Scienza. Characterizations of differentiability for h-convex functions in stratified groups
    Ann. Sc. Norm. Super. Pisa Cl. Sci., vol. 13, 675-697, (2014)

  21. A. Bonfiglioli, E. Lanconelli, V. Magnani and M. Scienza. H-convex distributions in stratified groups
    Proc. Amer. Math. Soc., vol. 141, n.10, 3633-3638, (2013)

  22. V. Magnani. Towards Differential Calculus in stratified groups
    J. Aust. Math. Soc., vol. 95, n.1, 76-128, (2013)

  23. R. Korte and V. Magnani. Measure of curves in graded groups
    Illinois J. Math., vol. 56, n.2, 353-366, (2012)

  24. V. Magnani. An area formula in metric spaces
    Colloq. Math., vol. 124, 275-283, (2011)

  25. G.P. Leonardi and V. Magnani. Intersections of intrinsic submanifolds in the Heisenberg group
    J. Math. Anal. Appl., vol. 378, n.1, 98-108, (2011)

  26. V. Magnani. Area implies coarea
    Indiana Univ. Math. J., vol. 60, 77-100, (2011)

  27. V. Magnani. Contact equations, Lipschitz extensions and isoperimetric inequalities
    Calc. Var. Partial Differential Equations, vol. 39, 233-271, (2010)

  28. E. Le Donne and V. Magnani. Measure of submanifolds in the Engel group
    Rev. Mat. Iberoamericana, vol. 26, n.1, 333-346, (2010)

  29. V. Magnani. Blow-up estimates at horizontal points and applications
    J. Geom. Anal., vol. 20, n.3, 705-722, (2010)

  30. V. Magnani. Nonexistence of horizontal Sobolev surfaces in the Heisenberg group
    Proc. Amer. Math. Soc., vol. 138, 1785-1791, (2010)

  31. V. Magnani. Non-horizontal submanifolds and coarea formula
    J. Anal. Math., vol. 106, 95-127, (2008)

  32. V. Magnani and D. Vittone. An intrinsic measure for submanifolds in stratified groups
    J. Reine Angew. Math., vol. 619, 203-232, (2008)

  33. V. Magnani. Lipschitz continuity, Aleksandrov theorem and characterizations for H-convex functions
    Math. Ann., vol. 334, n.1, 199-233, (2006)

  34. V. Magnani. Characteristic points, rectifiability and perimeter measure on stratified groups
    J. Eur. Math. Soc., vol. 8, n.4, 585-609, (2006)

  35. V. Magnani. Blow-up of regular submanifolds in Heisenberg groups and applications
    Cent. Eur. J. Math., vol. 4, n.1, 82-109, (2006)

  36. V. Magnani. Differentiability from representation formula and Sobolev-Poincarè inequality
    Studia Math., vol. 168, n.3, 251-272, (2005)

  37. V. Magnani. The coarea formula for real-valued Lipschitz maps on stratified groups
    Math. Nachr., vol. 278, n.14, 1689-1705, (2005)

  38. V. Magnani. Unrectifiability and rigidity in stratified groups
    Arch. Math., vol. 83, n.6, 568-576, (2004)

  39. V. Magnani. Note on coarea formulae in the Heisenberg group
    Publ. Mat., vol. 48, n.2, 409-422, (2004)

  40. L. Ambrosio and V. Magnani. Weak differentiability of BV functions on stratified groups
    Math. Z., vol. 245, 123-153, (2003)

  41. B. Kirchheim and V. Magnani. A counterexample to metric differentiability
    Proc. Ed. Math. Soc., vol. 46, 221-227, (2003)

  42. V. Magnani. A blow-up theorem for regular hypersurfaces on nilpotent groups
    Manuscripta Math., vol. 110, n.1, 55-76, (2003)

  43. V. Magnani. On a general coarea inequality and applications
    Ann. Acad. Sci. Fenn. Math., vol. 27, 121-140, (2002)

  44. V. Magnani. Differentiability and Area formula on stratified Lie groups
    Houston J. Math., vol. 27, n.2, 297-323, (2001)

Expository papers

  1. V. Magnani. Lipschitz estimates for convex functions with respect to vector fields
    Bruno Pini Mathematical Analysis Seminar, Vol. 1 (2012) pp. 60-71

  2. V. Magnani. Spherical Hausdorff measure of submanifolds in Heisenberg groups
    Ricerche Mat., vol. 54, n.2, 607-613 (2006)

  3. V. Magnani. Convexity in Carnot groups
    Partielle Differentialgleichungen, pp 11-16, Oberwolfach, vol. 2. Report 33, (2005)