Acta Mathematica Sinica, English Series

, Volume 33, Issue 11, pp 1565–1568 | Cite as

Every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence Riemannian manifolds

  • Yong Hong Huang


In this paper, we will show that every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds.


Riemannian manifold Sub-Riemannian manifold Gromov–Hausdorff convergence 

MR(2010) Subject Classification

53C17 53C23 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



I wish to thank my supervisor of postgraduate Professor Fuquan Fang for introducing me in the study of the sub-Riemannian geometry.


  1. [1]
    Agrachev, A.: Some open problems. In: Geometric Control Theory and Sub-Riemannian Geometry, Volume 5 of the series Springer INdAM Series, pp. 1–13, 2014Google Scholar
  2. [2]
    Agrachev, A., Barilari, D., Boscain, U.: Introduction to Riemannian and Sub-Riemannian Geometry, Preprint SISSA, 2013MATHGoogle Scholar
  3. [3]
    Agrachev, A., Barilari, D., Boscain, U.: On the Hausdorff volume in sub-Riemannian geometry. Calc. Var. Partial Differentia. Equations, 43, 355–388 (2012)MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Agrachev, A., Lee, P.: Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Math. Ann., 360, 209–253 (2014)MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Agrachev, A., Lee, P.: Optimal transportation under nonholonomic constraints. Trans. Amer. Math. Soc., 361, 6019–6047 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Burago, D., Burago, Y., Ivanov, S.: A Course in Metric Geometry. Graduate Studies in Mathematics (Book 33), American Mathematical Society, Providence, RI, 2001MATHGoogle Scholar
  7. [7]
    Donne, E. L.: Lipschitz and path isometric embeddings of metric spaces. Geometria. Dedicata, 166, 47–66 (2013)MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Do Carmo, D. P.: Riemannian Geometry, Mathematics: Theory and Applications, Birkhauser, Boston, 1992Google Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mathematical ScienceCapital Normal UniversityBeijingP. R. China
  2. 2.Qiannan Preschool Education College for NationalitiesGuiding County of Guizhou ProvinceGuizhouP. R. China

Personalised recommendations