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  • Séminaire de théorie spectrale et géométrie
  • Volume 33 (2015-2016)
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On measures in sub-Riemannian geometry
Roberta Ghezzi1; Frédéric Jean2
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, Volume 33 (2015-2016), pp. 17-46.
  • Abstract

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.

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Published online: 2018-08-27
DOI: 10.5802/tsg.312
Author's affiliations:
Roberta Ghezzi 1; Frédéric Jean 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)
  • BibTeX
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@article{TSG_2015-2016__33__17_0,
     author = {Roberta Ghezzi and Fr\'ed\'eric Jean},
     title = {On measures in {sub-Riemannian} geometry},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {17--46},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     year = {2015-2016},
     doi = {10.5802/tsg.312},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.312/}
}
TY  - JOUR
AU  - Roberta Ghezzi
AU  - Frédéric Jean
TI  - On measures in sub-Riemannian geometry
JO  - Séminaire de théorie spectrale et géométrie
PY  - 2015-2016
SP  - 17
EP  - 46
VL  - 33
PB  - Institut Fourier
PP  - Grenoble
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.312/
DO  - 10.5802/tsg.312
LA  - en
ID  - TSG_2015-2016__33__17_0
ER  - 
%0 Journal Article
%A Roberta Ghezzi
%A Frédéric Jean
%T On measures in sub-Riemannian geometry
%J Séminaire de théorie spectrale et géométrie
%D 2015-2016
%P 17-46
%V 33
%I Institut Fourier
%C Grenoble
%U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.312/
%R 10.5802/tsg.312
%G en
%F TSG_2015-2016__33__17_0
Roberta Ghezzi; Frédéric Jean. On measures in sub-Riemannian geometry. Séminaire de théorie spectrale et géométrie, Volume 33 (2015-2016), pp. 17-46. doi : 10.5802/tsg.312. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.312/
  • References
  • Cited by

[1] Andrei Agrachev; Davide Barilari; Ugo Boscain 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] Andrei Agrachev; Davide Barilari; Ugo Boscain 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] Andrei Agrachev; Ugo Boscain; Jean-Paul Gauthier; Francesco Rossi 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] Davide Barilari; Luca Rizzi A formula for Popp’s volume in sub-Riemannian geometry, Anal. Geom. Metr. Spaces, Volume 1 (2013), pp. 42-57 | DOI | MR | Zbl

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

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

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

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

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

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

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

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

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

[16] Leon Simon 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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