On measures in sub-Riemannian geometry
Ghezzi, Roberta1 ; Jean, Frédéric2
1 Institut de Mathématiques de Bourgogne UBFC 9 Avenue Alain Savary BP47870 21078 Dijon Cedex (France)
2 Unité de Mathématiques Appliquées, ENSTA ParisTech Université Paris-Saclay 91120 Palaiseau (France)
Séminaire de théorie spectrale et géométrie, Tome 33 (2015-2016), pp. 17-46.

In [9] we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions.

Publié le :
DOI : 10.5802/tsg.312
Ghezzi, Roberta 1 ; Jean, Frédéric 2

1 Institut de Mathématiques de Bourgogne UBFC 9 Avenue Alain Savary BP47870 21078 Dijon Cedex (France)
2 Unité de Mathématiques Appliquées, ENSTA ParisTech Université Paris-Saclay 91120 Palaiseau (France) 
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Ghezzi, Roberta; Jean, Frédéric. On measures in sub-Riemannian geometry. Séminaire de théorie spectrale et géométrie, Tome 33 (2015-2016), pp. 17-46. doi : 10.5802/tsg.312. http://archive.numdam.org/articles/10.5802/tsg.312/

[1] Agrachev, Andrei; Barilari, Davide; Boscain, Ugo On the Hausdorff volume in sub-Riemannian geometry, Calc. Var. Partial Differ. Equ., Volume 43 (2012) no. 3-4, pp. 355-388 | DOI | MR | Zbl

[2] Agrachev, Andrei; Barilari, Davide; Boscain, Ugo Introduction to Riemannian and sub-Riemannian geometry (from a Hamiltonian viewpoint) (2016) (Lecture notes available at http://webusers.imj-prg.fr/~davide.barilari/Notes.php, preprint SISSA 09/2012/M. Version Nov 20)

[3] Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups, J. Funct. Anal., Volume 256 (2009) no. 8, pp. 2621-2655 | DOI | MR | Zbl

[4] Barilari, Davide; Rizzi, Luca A formula for Popp’s volume in sub-Riemannian geometry, Anal. Geom. Metr. Spaces, Volume 1 (2013), pp. 42-57 | DOI | MR | Zbl

[5] Bellaïche, André The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry (Progress in Mathematics), Volume 144, Birkhäuser, 1996, pp. 1-78 | MR | Zbl

[6] Burago, Dmitri; Burago, Yuri; Ivanov, Sergei A course in metric geometry, Graduate Studies in Mathematics, 33, American Mathematical Society, 2001, xiv+415 pages | DOI | MR | Zbl

[7] Federer, Herbert Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, 153, Springer, 1969, xiv+676 pages | MR | Zbl

[8] Ghezzi, Roberta; Jean, Frédéric Hausdorff measure and dimensions in non equiregular sub-Riemannian manifolds, Geometric control theory and sub-Riemannian geometry (Springer INdAM Series), Volume 5, Springer, 2014, pp. 201-218 | DOI | MR | Zbl

[9] Ghezzi, Roberta; Jean, Frédéric Hausdorff volume in non equiregular sub-Riemannian manifolds, Nonlinear Anal., Volume 126 (2015), pp. 345-377 | DOI | MR | Zbl

[10] Gigli, Nicola; Mondino, Andrea; Savaré, Giuseppe Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows, Proc. Lond. Math. Soc., Volume 111 (2015) no. 5, pp. 1071-1129 | DOI | MR | Zbl

[11] Leonardi, Gian Paolo; Rigot, Séverine; Vittone, Davide Isodiametric sets in the Heisenberg group, Rev. Mat. Iberoam., Volume 28 (2012) no. 4, pp. 999-1024 | DOI | MR | Zbl

[12] Magnani, Valentino On a measure-theoretic area formula, Proc. Roy. Soc. Edinburgh Sect. A, Volume 145 (2015) no. 4, pp. 885-891 | DOI | MR | Zbl

[13] Montgomery, Richard A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, 91, American Mathematical Society, 2002, xx+259 pages | MR | Zbl

[14] Rifford, Ludovic Sub-Riemannian Geometry and Optimal Transport, SpringerBriefs in Mathematics, Springer, 2014, vii+140 pages | Zbl

[15] Rigot, Séverine Isodiametric inequality in Carnot groups, Ann. Acad. Sci. Fenn. Math., Volume 36 (2011) no. 1, pp. 245-260 | DOI | MR | Zbl

[16] Simon, Leon Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3, Australian National University Centre for Mathematical Analysis, 1983, vii+272 pages | MR | Zbl

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