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.
@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/
[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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