Full Professor, Università di Padova

Email: monti AT math.unipd.it

Available papers (55):

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• V. Franceschi - R. Monti - A. Socionovo (Preprint)
  Mean value formulas on surfaces in Grushin spaces (2023)
• F. Boarotto - R. Monti - F. Palmurella (Nonlinearity)
  Third order open mapping theorems and applications to the end-point map (2020)
• V. Franceschi - R. Monti - A. Righini - M. Sigalotti (Journal of Geometric Analysis)
  The isoperimetric problem for regular and crystalline norms in $\mathbb H^1$ (2020)
• E. Battaglia - R. Monti - A. Righini (Accepted Paper: Annali di Matematica Pura ed Applicata)
  Stable hypersurfaces in the complex projective space (2019)
• R. Monti - D. Morbidelli (Accepted Paper: Potential Analysis)
  John and uniform domains in generalized Siegel boundaries (2019)
• R. Monti - M. Zaccaron (Submitted Paper)
  Height estimate and Lipschitz approximation for geodesics in Carnot groups (2019)
• V. Franceschi - F. Montefalcone - R. Monti (Accepted Paper: Analysis and Geometry in Metric Spaces)
  CMC spheres in the Heisenberg group (2019)
• E. Battaglia - F. Montefalcone - R. Monti (Submitted Paper)
  Stability of hypersurfaces in the complex hyperbolic space (2019)
• D. Gerosa - R. Monti - D. Morbidelli (Accepted Paper: Cont. Math.)
  A trace theorem for Martinet-type vector fields (2018)
• R. Monti - A. Pigati - D. Vittone (SIAM J. Control Optim. 56 (2018))
  On tangent cones to length minimizers in Carnot-Carathéodory spaces (2018)
• R. Monti - A. Pigati - D. Vittone (Calc. Var. Partial Differential Equations 57)
  Existence of tangent lines to Carnot-Carathéodory geodesics (2018)
• R. Monti (Proceedings: Bruno Pini Mathematical Analysis Seminar, 2018, 9, 137--146)
  The regularity problem for geodesics of the control distance (2018)
• E. Le Donne - G. P. Leonardi - R. Monti - D. Vittone (Comm. Anal. and Geom.)
  Extremal polynomials in stratified groups (2018)
• M. Fogagnolo - R. Monti - D. Vittone (Ann. Ac. Sci. Fennicae)
  Variation formulas for H-rectifiable sets (2017)
• R. Monti - G. Stefani (J. Math. Pures Appl.)
  Improved Lipschitz Approximation of $H$-perimeter minimizing boundaries (2017)
• R. Monti (Accepted Paper: Nonlinear Analysis Series A: Theory, Methods & Applications)
  Minimal surfaces and harmonic functions in the Heisenberg group (2015)
• V. Franceschi - G. P. Leonardi - R. Monti (Calc. Var. Partial Differential Equations)
  Quantitative isoperimetric inequalities in $\mathbb H ^n$ (2015)
• R. Monti - D. Vittone (Analysis and PDE)
  Height estimate and slicing formulas in the Heisenberg group (2015)
• E. Le Donne - G. P. Leonardi - R. Monti - D. Vittone (ESAIM Control Optim. Calc. Var.)
  Corners in non-equiregular sub-Riemannian manifolds (2015)
• R. Monti (Lecture notes)
  Isoperimetric problem and minimal surfaces in the Heisenberg group (2014)
• V. Franceschi - R. Monti (Accepted Paper: Revista Matemática Iberoabericana)
  Isoperimetric Problem in H-type groups and Grushin spaces (2014)
• R. Monti (Accepted Paper: J. Geom. Anal.)
  Rearrangements in metric spaces and in the Heisenberg group (2013)
• R. Monti (Accepted Paper: Calc. Var.)
  Regularity results for sub-Riemannian geodesics (2013)
• R. Monti (Accepted Paper: Ann. Mat. Pura Appl.)
  A family of nonminimizing abnormal curves (2013)
• R. Monti (Calc. Var.)
  Lipschitz approximation of H-perimeter minimizing boundaries (2013)
• R. Monti (Springer INDAM Series)
  The regularity problem for sub-Riemannian geodesics (2013)
• E. Le Donne - G. P. Leonardi - R. Monti - D. Vittone (GAFA Geometric and Functional Analysis)
  Extremal curves in nilpotent Lie groups (2013)
• R. Monti - D. Vittone (Math. Z.)
  Sets with finite $\mathbb H$-perimeter and controlled normal (2012)
• Z. Balogh - R. Monti - J. Tyson (J. Math. Pures Appl.)
  Frequency of Sobolev and quasiconformal dimension distortion (2012)
• R. Monti - D. Morbidelli (Submitted Paper)
  Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids (2010)
• R. Monti - D. Morbidelli (Accepted Paper: J. Math. Soc. Jap.)
  Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids (2010)
• G. Arena - A. O. Caruso - R. Monti (Submitted Paper)
  Regularity properties of H-convex sets (2010)
• Z. Balogh - R. Berger - R. Monti - J. Tyson (Math. Proc. Cambridge Philos. Soc.)
  Exceptional sets for self-similar fractals in Carnot groups (2010)
• G. Arena - A. O. Caruso - R. Monti (Accepted Paper: J. Geom. Analysis)
  "Regularity properties of $H$--convex sets" (2010)
• Z. Balogh - R. Berger - R. Monti - J. T. Tyson (Math. Proc. Camb. Phil. Soc)
  Exceptional sets for self-similar fractals in Carnot groups (2010)
• R. Monti (Accepted Paper: Adv. Calc. Var. )
  Heisenberg isoperimetric problem. The axial case (2008)
• R. Monti - D. Morbidelli (Proc. AMS)
  Positive solutions of anisotropic Yamabe--type equations in $R^n$ (2008)
• R. Monti - F. Serra Cassano - D. Vittone (Boll. Unione Mat. Ital. (9))
  A negative answer to the Bernstein problem for intrinsic graphs in the Heisenberg group (2008)
• R. Monti - M. Rickly (Accepted Paper: Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
  Convex isoperimetric sets in the Heisenberg group (2008)
• R. Monti - D. Morbidelli (Accepted Paper: Journal fuer die Reine und Angewandte Mathematik)
  Levi umbilical surfaces in complex space (2006)
• G. P. Leonardi - R. Monti (Accepted Paper: GAFA)
  End-point equations and regularity of sub-Riemannian geodesics (2006)
• R. Monti (Accepted Paper: Comm. Part. Diff. Eq.)
  Sobolev inequalities for weighted gradients (2005)
• R. Monti - D. Morbidelli (Accepted Paper: Duke Math. J.)
  Kelvin transform for Grushin operators and critical semilinear equations (2005)
• R. Monti - M. Rickly (Accepted Paper: J. Convex Anal.)
  Geodetically convex sets in the Heisenberg group (2004)
• Z. Balogh - R. Monti (Proc. Amer. Math. Soc. )
  Accessible domains in the Heisenberg group (2004)
• R. Monti - D. Morbidelli (Accepted Paper: Indiana Univ. Math. J.)
  Non tangentially accesible domains for vector fields (2004)
• R. Monti - D. Morbidelli (Accepted Paper: Trans. AMS)
  Regular domains in homogeneous groups (2004)
• R. Monti - F. Serra Cassano (J. Convex Anal.)
  Degenerate perturbations of a two-phase transition model (2003)
• R. Monti - D. Morbidelli (Math. Z.)
  Trace theorems for vector fields (2003)
• R. Monti - D. Morbidelli (Accepted Paper: J. Geom. Anal.)
  Isoperimetric inequality in the Grushin plane (2003)
• R. Monti (Ann. Acad. Sci. Fenn. Math.)
  Brunn-Minkowski and isoperimetric inequality in the Heisenberg group (2003)
• R. Monti - D. Morbidelli (Accepted Paper: Jour. Anal. Math.)
  John domains for the control distance of diagonal vector fields (2003)
• R. Monti - F. Serra Cassano (Calc. Var. Partial Differential Equations)
  Surface measures in Carnot- Caratheodory spaces (2001)
• R. Monti (Phd Thesis)
  Distances, boundaries and surface measures in Carnot-Caratheodory spaces (2001)
• R. Monti (Accepted Paper: Rend. Lincei)
  Some properties of Carnot-Caratheodory balls in the Heisenberg group (2000)

Seminars:

• 30 sep 2013: Isoperimetric problem and minimal surfaces in the Heisenberg group
• 20 mar 2013: The regularity problem for sub-Riemannian geodesics
• 24 nov 2010: Riarrangiamenti in spazi metrici
• 16 apr 2008: Riarrangiamenti per misure perimetro nel piano
• 25 jan 2007: The isoperimetric problem in the Heisenberg group: the convex case

Speaker:

• 11 jun 2018 - 15 jun 2018: Geometric Measure Theory in Verona
• 17 oct 2017 - 18 oct 2017: Sub-Riemannian days 2017
• 20 jun 2016 - 23 jun 2016: Singular Phenomena and Singular Geometries
• 9 jun 2016 - 10 jun 2016: Two-day Meeting on linear and nonlinear PDE's in honor of the 65th birthday of Cristian Gutierrez
• 4 mar 2015 - 6 mar 2015: Mini-courses and workshop on Geometric Analysis in the Heisenberg group
• 16 jun 2014 - 20 jun 2014: Eighth School on Analysis and Geometry in Metric Spaces
• 30 sep 2013 - 4 oct 2013: ERC-School on Geometric Measure Theory and Real Analysis
• 10 oct 2011 - 14 oct 2011: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Organizer:

• 6 sep 2021 - 7 sep 2021: PaPa - Padua Paris sub-Riemannian seminar
• 23 jun 2014 - 27 jun 2014: Mini-courses in Mathematical Analysis 2014
• 10 jun 2013 - 14 jun 2013: Mini-courses in Mathematical Analysis 2013
• 18 jun 2012 - 22 jun 2012: Mini-courses in Mathematical Analysis 2012