RIGOT Séverine
Professeure
Laboratoire de Mathématiques J.A. Dieudonné
Université Côte d'Azur

  Severine.RIGOT(at)univ-cotedazur.fr    +33 4 89 15 05 38     Bureau 607


Research interests

• Analysis and Geometry on Metric Spaces
• Geometric Measure Theory
• Calculus of Variations
• Sub-Riemannian Geometry

Member of

• ANR GEOMETRYA
• ANR SRGI (Sub-Riemannian Geometry and Interactions)
• GDR AFHP (Analyse Fonctionnelle, Harmonique et Probabilités)
• GDR CALVA (Calcul des variations et théorie géométrique de la mesure)
  

Publications and Preprints

• Monotone sets and local minimizers for the perimeter in Carnot groups, Nonlinear Anal., Volume 237 (2023).
• Precisely monotone sets in step-2 rank-3 Carnot algebras, with D. Morbidelli, Math. Z., 303, 3 (2023), 54, full-text view-only version here.
• Horizontally affine functions on step-2 Carnot algebras, with E. Le Donne and D. Morbidelli, J. Geom. Anal. 33, 359 (2023).
• Differentiation of measures in metric spaces, New Trends on Analysis and Geometry in Metric Spaces, Springer, 2022, Lecture Notes in Mathematics (LNM, volume 2296), C.I.M.E. Foundation Subseries (LNMCIME, volume 2296)
• Quantitative notions of rectifiability in the Heisenberg groups, arXiv:1904.06904
• Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group, with K. Fässler and T. Orponen, Trans. Amer. Math. Soc. 373 (2020), no. 8, 5957-5996.
• The Besicovitch covering property in the Heisenberg group revisited, with S. Golo, J. Geom. Anal. 29 (2019), no. 4, 3345-3383.
  
• Besicovitch Covering Property on graded groups and applications to measure differentiation, with E. Le Donne, J. Reine Angew. Math. 750 (2019), 241-297.
• Besicovitch Covering Property for homogeneous distances in the Heisenberg groups, with E. Le Donne, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 5, 1589-1617.
  
• Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher, with E. Le Donne, Proc. Amer. Math. Soc. 144 (2016), no. 5, 2003-2013.
• Isodiametric sets in the Heisenberg group, with G.P. Leonardi and D. Vittone, Rev. Mat. Iberoam. 28 (2012), no. 4, 999–1024.
  
• Isodiametric inequality in Carnot groups, Ann. Acad. Sci. Fenn. Math. Volumen 36, 2011, 245–260.
  
• Monge's transport problem in the Heisenberg group, with L. De Pascale, Adv. Calc. Var. 4 (2011), no. 2, 195–227.
• Lipschitz Non-extension Theorems into Jet Space Carnot Groups, with S. Wenger, Int. Math. Res. Not. IMRN 2010, no. 18, pp. 3633–3648.
• Quasiminimal partitions with prescribed measure, SIAM J. Math. Anal. 37 (2006), no. 5, 1589-1615.
• Mass transportation in groups of type H, Commun. Contemp. Math. 7 (2005), no. 4, pp 509-537.
• Transport optimal de mesure dans le groupe de Heisenberg, Séminaire de Théorie Spectrale et Géométrie, Vol. 22, Année 2003-2004, 9--23. Univ. Grenoble I, 2004.
  
• Counter example to the Besicovitch covering property for some Carnot groups equipped with their Carnot-Carathéodory metric, Math. Z. 248 (2004), no. 4, 827-848.
  
• Optimal mass transportation in the Heisenberg group, with L. Ambrosio, J. Funct. Anal. 208 (2004), no. 2, 261-301.
• Quasiminimal crystals with a volume constraint and uniform rectifiability, J. Math. Pures Appl. (9) 82 (2003), no. 12, pp 1651-1695.
• Isoperimetric sets on Carnot groups, with G.P. Leonardi, Houston J. Math. 29 (2003), no. 3, pp 609-637.
• Ensembles quasiminimaux pour le périmètre et rectifiabilité uniforme, Sémin. Équ. Dériv. Partielles, 2000-2001,  Exp. No. IX, 13 pp., École Polytech., Palaiseau, 2001.
  
• Ensembles quasiminimaux pour le périmètre et rectifiabilité uniforme, Mém. Soc. Math. Fr. (N.S.)  82 (2000), v+104pp.
• Uniform Partial Regularity of Quasi Minimizers for the Perimeter, Calc. Var. Partial Differential Equations 10 (2000), no. 4, 389-406.
• Big Pieces of $C^{1,\alpha}$-Graphs for Minimizers of the Mumford-Shah Functional, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29 (2000), no. 2, 329-349.