SubRiemannian Geometry Page

All the following articles and books have links either to the author's webpage, or to the publishing journal, or to google book. Hence there has no been any violation of author's or publisher's rights.

Here you can find:

       1  Material for an introduction to subRiemannian metrics                                                            

       2  Extra material for the subRiemannian seminars                                                            

       1  Material for an introduction to subRiemannian metrics                                                            

A. Agrachev, D. Barilari, and U. Boscain, Introduction to Riemannian and Sub-Riemannian geometry (from Hamiltonian viewpoint)

D. Burago, Y. Burago, and S. Ivanov, A course in metric geometry, Graduate Studies in Mathematics, vol. 33, American Mathematical Society, Providence, RI,2001.

A. Bellaïche, The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry, Progr. Math., vol. 144, Birkhäuser, Basel, 1996, pp. 1–78.

M. Gromov. Groups of polynomial growth and expanding maps. Inst. Hautes  Etudes Sci. Publ. Math., (53):53{73,

1981.

M. Gromov, Carnot-Carathéodory spaces seen from within, Sub-Riemannian geometry, Progr. Math., vol. 144, Birkhäuser, Basel, 1996, pp. 79–323.

M. Gromov. Metric structures for Riemannian and non-Riemannian spaces, volume 152 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, 1999. Based on the 1981 French original, With appendices by M. Katz, P. Pansu and S. Semmes, Translated from the French by Sean Michael Bates.

J. Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001.

S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Graduate Studies in Mathematics, vol. 34, American Mathematical Society, Providence, RI, 2001, Corrected reprint of the 1978 original.

A. Knapp, Lie groups beyond an introduction, second ed., Progress in Mathematics, vol. 140, Birkhäuser Boston Inc., Boston, MA, 2002.

E. Le Donne. Lecture notes on sub-Riemannian geometry. Preprint, 2010.

J. Mitchell, On Carnot-Carathéodory metrics, J. Differential Geom. 21 (1985), no. 1, 35–45.

G. Margulis and G. Mostow, The differential of a quasi-conformal mapping

of a Carnot-Carathéodory space, Geom. Funct. Anal. 5 (1995), no. 2, 402–433.

R. Montgomery, A tour of subriemannian geometries, their geodesics and applications,

Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002.

P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2) 129 (1989), no. 1, 1–60.

P. Pansu. Croissance des boules et des geodesiques fermees dans les nilvarietes. Ergodic Theory Dynam. Systems, 3(3):415{445, 1983.

M. S. Raghunathan. Discrete subgroups of Lie groups. Springer-Verlag, New York, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68.

       2  Extra material for the subRiemannian seminars                                                            

A. A. Agrachev, Any sub-Riemannian metric has points of smoothness, Dokl. Akad. Nauk 424 (2009), no. 3, 295{298. MR 2513150 (2010i:53050)

L. Ambrosio, B. Kleiner, and E. Le Donne, Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane, J. Geom. Anal. 19 (2009), no. 3, 509-540.

V. Berestovski, Homogeneous manifolds with an intrinsic metric. I, Sibirsk. Mat. Zh. 29 (1988), no. 6, 17{29.

C. Bellettini and E. Le Donne, Regularity of sets with constant horizontal normal in the Engel group, Preprint (2011).

E. Breuillard, Geometry of locally compact groups of polynomial growth and shape of large balls, Preprint (2007).

J. Cheeger and T. Colding, On the structure of spaces with Ricci curvature bounded below. I, J. Dierential Geom. 46 (1997), no. 3, 406-480.

J. Cheeger and B. Kleiner, On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces, Inspired by S. S. Chern, Nankai Tracts Math., vol. 11, World Sci. Publ., Hackensack, NJ, 2006, pp. 129-152.

J. Cheeger and B. Kleiner,Differentiating maps into L1, and the geometry of BV functions, Ann. of Math. (2)171 (2010), no. 2, 1347-1385.

J. Cheeger and B. Kleiner, Metric differentiation, monotonicity and maps to L1, Invent. Math. 182 (2010), no. 2, 335{370.

B. Franchi, R. Serapioni, and F. Serra Cassano, Rectifiability and perimeter in the Heisenberg group, Math. Ann. 321 (2001), no. 3, 479-531.

B. Franchi, R. Serapioni, and F. Serra Cassano, On the structure of finite perimeter sets in step 2 Carnot groups, J. Geom. Anal. 13 (2003), no. 3, 421{466.

E. Le Donne, Lipschitz and path isometric embeddings of metric spaces, Preprint, submitted (2010).

E. Le Donne, Geodesic manifolds with a transitive subset of smooth biLipschitz maps, Groups, Geometry, and Dynamics 5 (2011), no. 3.

E. Le Donne, Geodesic metric spaces with unique blow-up almost everywhere: properties and examples, Preprint, submitted (2011).

E. Le Donne, Metric spaces with unique tangents, Ann. Acad. Sci. Fenn. Math. 36 (2011).

E. Le Donne, A. Ottazzi, and B. Warhurst, Ultrarigid tangents of sub-Riemannian nilpotent groups, Preprint, submitted (2011).

W. Liu and H. Sussman, Shortest paths for sub-Riemannian metrics on rank-two distributions, Mem. Amer. Math. Soc. 118 (1995), no. 564, x+104.

P. Mattila, Measures with unique tangent measures in metric groups, Math. Scand. 97 (2005), no. 2, 298{308.

R. Montgomery, Abnormal minimizers, SIAM J. Control Optim. 32 (1994), no. 6, 1605-1620.

S. Pauls, The large scale geometry of nilpotent Lie groups, Comm. Anal. Geom. 9 (2001), no. 5, 951-982.

L. Rothschild and E. Stein. Hypoelliptic differential operators and nilpotent groups. Acta Math., 137(3-4):247-320, 1976.