Roberto Monti

• Regularity of sub-Riemmanian geodesics

1. F. Boarotto, R. Monti, F. Palmurella, Third order open mapping theorems and applications to the end-point map, 2019
2. R. Monti, M. Zaccaron, Height estimate and Lipschitz approximation for geodesics in Carnot groups, 2019 (to appear)
3. R. Monti, The regularity problem for geodesics of the control distance. Bruno Pini Mathematical Analysis Seminar, 2018, 9,  137--146
4. R. Monti, A. Pigati, D. Vittone, Tangent lines to CC length-minimizing curves, submitted 2016
5. E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone, Extremal polynomials in stratified groups,  Communications in Analysis and Geometry, accepted 2016
6. E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone, Corners in non-equiregular sub-Riemannian manifolds. ESAIM Control Optim. Calc. Var. 21 (2015), no. 3, 625-634
7. R. Monti, The regularity problem for sub-Riemannian geodesics, Springer INDAM Series 2013
8. R. Monti, A family of nonminimizing abnormal curves, Ann. Mat. Pura Appl. 2013
9. R. Monti, Regularity results on sub-Riemannian geodesics, Calc. Var. 2013
10. E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone, Extremal curves in nilpotent Lie groups, GAFA 2013
11. G. L. Leonardi, R. Monti, End-point equations and regularity of sub-Riemannian geodesics,  GAFA 18  (2008),  no. 2, 552-582

• Isoperimetric problems

1. V. Franceschi, F. Montefalcone, R. Monti, Constant Mean Curvature spheres in  H^1, submitted 2016
2. V. Franceschi, R. Monti, Isoperimetric problem in H-type groups and Grushin spaces, Revista Mat. Iberoam. (to appear) 2016
3. V. Franceschi, R. Monti, G. P. Leonardi, Quantitative isoperimetric inequalities in H^n, Calc. Var. Partial Differential Equations 54 (2015), no. 3, 3229-3239
4. R. Monti, Isoperimetric problem and minimal surfaces in the Heisenberg group, in Geometric Measure Theory and Real Analysis, pp. 57--130, L. Ambrosio Ed.,  CRM Series, Vol. 17 (2015)
5. R. Monti, Heisenberg isoperimetric problem. The axial case, Adv. Calc. Var. 1 (2008), 93-121
6. R. Monti, D. Morbidelli, Isoperimetric inequality in the Grushin plane.  J. Geom. Anal.  14 (2004),  no. 2, 355-368
7. R. Monti, Brunn-Minkowski and isoperimetric inequality in the Heisenberg group, Ann. Acad. Sci. Fenn. Math.  28 (2003), 99-109

• Regular domains and trace theorems

1. R. Monti, D. Morbidelli, John and uniform domains in generalized Siegel boundaries, Cont. Math. 2019 (to appear)
2. D. Gerosa, R. Monti, D. Morbidelli, Trace theorem for the Martinet distribution, Pot. Anal. 2019 (to appear)
3. R. Monti, D. Morbidelli, Regular domains in homogeneous groups, Trans. Amer. Math. Soc.   357  (2005), no. 8, 2975-3011
4. R. Monti, D. Morbidelli, Non-tangentially accessible domains for vector fields.  Indiana Univ. Math. J.  54  (2005),  no. 2, 473-498
5. Z. Balogh, R. Monti, Accessible domains in the Heisenberg group, Proc. Amer. Math. Soc. 132, No.1, 97-106 (2004)
6. R. Monti, D. Morbidelli, John domains for the control distance of diagonal vector fields, J. Anal. Math.  92  (2004), 259-284
7. R. Monti, D. Morbidelli, Trace theorems for vector fields, Math. Z.  239 (2002), 747-776

• Regularity of H-Minimal surfaces

1. R. Monti, G. Stefani, Improved Lipschitz approximation of H-perimeter minimizing boundaries, submitted 2016
2. M. Fogagnolo, R. Monti, D. Vittone, Variation formulas for H-rectifiable sets, Annales Academiae Scientiarum Fennicae, accepted 2016
3. R. Monti,  Minimal surfaces and harmonic functions in the Heisenberg group. Nonlinear Anal. 126 (2015), 378-393
4. R. Monti, D. Vittone, Height estimate and slicing formulas in the Heisenberg group. Anal. PDE 8 (2015), no. 6, 1421-1454
5. R. Monti, Lipschitz approximation of H-perimeter minimizing boundaries, Calc. Var. 2013
6. R. Monti, Rearrangements in metric spaces and in the Heisenberg group,  J. Geom. Anal. 2013
7. R. Monti, D. Vittone, Sets with finite H-perimeter and controlled normal, Math. Z. 270 (2012), 351-367

• Heisenberg group and CC-spaces

1. G. Arena, A.O. Caruso, R. Monti, Regularity properties of H-convex sets, J. Geom. Anal. 22 (2012), 583-602
2. Z. Balogh, R. Berger, R. Monti, J. Tyson,  Exceptional sets for the self-similar dimension in Carnot groups, Math. Proc. Camb. Phil. Soc. 149 (2010), 147-172
3. R. Monti, M. Rickly, Convex isoperimetric sets in the Heisenberg group, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)  8  (2009),  no. 2, 391-415
4. R. Monti, F. Serra Cassano, D. Vittone, A negative answer to the Bernstein problem for intrinsic graphs in the Heisenberg group, Boll. Unione Mat. Ital. (9)  1  (2008),  no. 3, 709-727
5. R. Monti, M. Rickly, Geodetically convex sets in the Heisenberg group, J. Convex Anal.  12  (2005),  no. 1, 187-196
6. R. Monti, F. Serra Cassano, Degenerate perturbations of a two-phase transition model. J. Convex Anal. 10 (2003), no. 1, 1-34
7. R. Monti, F. Serra Cassano, Surface measures in Carnot-Caratheodory spaces, Calc. Var. 13 (2001), no. 3, 339-376
8. R. Monti, Some properties of Carnot-Caratheodory balls in the Heisenberg group, Rend. Mat. Accad. Lincei, s.9 v.11 (2000) 155-167

• Semilinear PdEs and functional inequalities

1. R. Monti, D. Morbidelli, Positive solutions of anisotropic Yamabe-type equations in R^n,  Proc. Amer. Math. Soc.  136  (2008),  no. 12, 4295-4304
2. R. Monti, Sobolev inequalities for weighted gradients, Comm. Part. Diff. Eq. 31 (2006), 1479-1504
3. R. Monti, D. Morbidelli, Kelvin transform for Grushin operators and semilinear critical equations, Duke Math. J. 131, no.  1 (2006), 167-202

• Problems in complex space

1. R. Monti, D. Morbidelli, Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids, Journal of the Math. Soc. Jap. 64 (2012), 153-179
2. R. Monti, D. Morbidelli, Levi umbilical surfaces in complex space, J. Reine Angew. Math. 603 (2007),  113-131

• Quasiconformal mappings

1. Z. Balogh, R. Monti, J. Tyson, Frequency of Sobolev and quasiconformal dimension distortion, J. Math. Pures Appl, on line 2012

  

• Academic works

  • R. Monti, Isoperimetric inequality, semilinear equations and regular domains in Grushin spaces, Habilitationsschrift, Bern 5 January 2004
  • R. Monti, Distances, boundaries and surface measures in Carnot-Carathéodory spaces,  PhD Thesis in Mathematics, Università di Trento, 2001. Advisor: Prof. F. Serra Cassano
  • R. Monti,  Teorema di Rellich-Kondrachov per spazi di Sobolev generalizzati, Degree Thesis  in Mathematics, Università di Bologna, 1997. Advisor: Prof. E. Lanconelli
  • R. Monti,  Husserl: evidenza e ragione, Degree Thesis in Philosophy, Università di Macerata, 1991. Advisor: Prof. F. Voltaggio

• Other publications  
  

• R. Monti, Ordine e disordine. Analisi epistemologica ed ideologica, in ``Chaos", Quaderni della Biblioteca di Chiaravalle, n. 5 (2001), 25--37
• R. Monti, Origini delle guerre e democrazia internazionale, in ``L'arte del conflitto", Quaderni del Consiglio Regionale delle Marche, n. 2 (1997), 121--141
• R. Monti, La teoria Husserliana dell'io trascendentale, Aquinas 36 (1993), 181--192