Research directions and papers
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Stable CMC hypersurfaces
- E. Battaglia, R. Monti, A. Righini, Stable hypersurfaces in the complex projective space, Ann. Mat. Pura Appl. 2019 (to appear)
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V. Franceschi, F. Montefalcone, R. Monti, CMC Spheres in the Heisenberg Group. Anal. Geom. Metr. Spaces 7 (2019), no. 1, 109--129
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Regularity of sub-Riemmanian geodesics
- F. Boarotto, R. Monti, F. Palmurella, Third order open mapping theorems and applications to the end-point map, 2019
- R. Monti, M. Zaccaron, Height estimate and Lipschitz approximation for geodesics in Carnot groups, 2019 (to appear)
- R. Monti, The regularity problem for geodesics of the control distance. Bruno Pini Mathematical Analysis Seminar, 2018, 9, 137--146
- R. Monti, A. Pigati, D. Vittone, Tangent lines to CC length-minimizing curves, submitted 2016
- E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone, Extremal polynomials in stratified groups, Communications in Analysis and Geometry, accepted 2016
- 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
- R. Monti, The regularity problem for sub-Riemannian geodesics, Springer INDAM Series 2013
- R. Monti, A family of nonminimizing abnormal curves, Ann. Mat. Pura Appl. 2013
- R. Monti, Regularity results on sub-Riemannian geodesics, Calc. Var. 2013
- E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone, Extremal curves in nilpotent Lie groups, GAFA 2013
- G. L. Leonardi, R. Monti, End-point equations and regularity of sub-Riemannian geodesics, GAFA 18 (2008), no. 2, 552-582
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Isoperimetric problems
- V. Franceschi, F. Montefalcone, R. Monti, Constant Mean Curvature spheres in H^1, submitted 2016
- V. Franceschi, R. Monti, Isoperimetric problem in H-type groups and Grushin spaces, Revista Mat. Iberoam. (to appear) 2016
- V. Franceschi, R. Monti, G. P. Leonardi, Quantitative isoperimetric inequalities in H^n, Calc. Var. Partial Differential Equations 54 (2015), no. 3, 3229-3239
- 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)
- R. Monti, Heisenberg isoperimetric problem. The axial case, Adv. Calc. Var. 1 (2008), 93-121
- R. Monti, D. Morbidelli, Isoperimetric inequality in the Grushin plane. J. Geom. Anal. 14 (2004), no. 2, 355-368
- R. Monti, Brunn-Minkowski and isoperimetric inequality in the Heisenberg group, Ann. Acad. Sci. Fenn. Math. 28 (2003), 99-109
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Regular domains and trace theorems
- R. Monti, D. Morbidelli, John and uniform domains in generalized Siegel boundaries, Cont. Math. 2019 (to appear)
- D. Gerosa, R. Monti, D. Morbidelli, Trace theorem for the Martinet distribution, Pot. Anal. 2019 (to appear)
- R. Monti, D. Morbidelli, Regular domains in homogeneous groups, Trans. Amer. Math. Soc. 357 (2005), no. 8, 2975-3011
- R. Monti, D. Morbidelli, Non-tangentially accessible domains for vector fields. Indiana Univ. Math. J. 54 (2005), no. 2, 473-498
- Z. Balogh, R. Monti, Accessible domains in the Heisenberg group, Proc. Amer. Math. Soc. 132, No.1, 97-106 (2004)
- R. Monti, D. Morbidelli, John domains for the control distance of diagonal vector fields, J. Anal. Math. 92 (2004), 259-284
- R. Monti, D. Morbidelli, Trace theorems for vector fields, Math. Z. 239 (2002), 747-776
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Regularity of H-Minimal surfaces
- R. Monti, G. Stefani, Improved Lipschitz approximation of H-perimeter minimizing boundaries, submitted 2016
- M. Fogagnolo, R. Monti, D. Vittone, Variation formulas for H-rectifiable sets, Annales Academiae Scientiarum Fennicae, accepted 2016
- R. Monti, Minimal surfaces and harmonic functions in the Heisenberg group. Nonlinear Anal. 126 (2015), 378-393
- R. Monti, D. Vittone, Height estimate and slicing formulas in the Heisenberg group. Anal. PDE 8 (2015), no. 6, 1421-1454
- R. Monti, Lipschitz approximation of H-perimeter minimizing boundaries, Calc. Var. 2013
- R. Monti, Rearrangements in metric spaces and in the Heisenberg group, J. Geom. Anal. 2013
- R. Monti, D. Vittone, Sets with finite H-perimeter and controlled normal, Math. Z. 270 (2012), 351-367
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Heisenberg group and CC-spaces
- G. Arena, A.O. Caruso, R. Monti, Regularity properties of H-convex sets, J. Geom. Anal. 22 (2012), 583-602
- 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
- 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
- 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
- R. Monti, M. Rickly, Geodetically convex sets in the Heisenberg group, J. Convex Anal. 12 (2005), no. 1, 187-196
- R. Monti, F. Serra Cassano, Degenerate perturbations of a two-phase transition model. J. Convex Anal. 10 (2003), no. 1, 1-34
- R. Monti, F. Serra Cassano, Surface measures in Carnot-Caratheodory spaces, Calc. Var. 13 (2001), no. 3, 339-376
- R. Monti, Some properties of Carnot-Caratheodory balls in the Heisenberg group, Rend. Mat. Accad. Lincei, s.9 v.11 (2000) 155-167
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Semilinear PdEs and functional inequalities
- R. Monti, D. Morbidelli, Positive solutions of anisotropic Yamabe-type equations in R^n, Proc. Amer. Math. Soc. 136 (2008), no. 12, 4295-4304
- R. Monti, Sobolev inequalities for weighted gradients, Comm. Part. Diff. Eq. 31 (2006), 1479-1504
- R. Monti, D. Morbidelli, Kelvin transform for Grushin operators and semilinear critical equations, Duke Math. J. 131, no. 1 (2006), 167-202
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Problems in complex space
- R. Monti, D. Morbidelli, Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids, Journal of the Math. Soc. Jap. 64 (2012), 153-179
- R. Monti, D. Morbidelli, Levi umbilical surfaces in complex space, J. Reine Angew. Math. 603 (2007), 113-131
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Quasiconformal mappings
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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
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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