Geodesics in the Heisenberg Group

References

[1] L. Ambrosio, S. Rigot, Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2004), 261–301. 10.1016/S0022-1236(03)00019-3Search in Google Scholar

[2] A. Bellaïche, The tangent space in sub-Riemannian geometry, in: A. Bellaïche, J.J. Risler (Eds.), Sub-Riemannian geometry, Progress in Mathematics, Vol. 144, Birkhäuser, Basel, 1996, pp. 1–78. 10.1007/978-3-0348-9210-0_1Search in Google Scholar

[3] V. N. Berestovskii, Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane. Siberian Math. J. 35 (1994), 1–8. Search in Google Scholar

[4] D. Burago, Y. Burago, S. Ivanov, A course in metric geometry. Graduate Studies inMathematics, 33. AmericanMathematical Society, Providence, RI, 2001. 10.1090/gsm/033Search in Google Scholar

[5] L. Capogna, S. D. Pauls, D. Danielli, J. T. Tyson, An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, Progress in Mathematics, Vol. 259. Birkhäuser Basel. 2007. Search in Google Scholar

[6] H. Dym, H. P. McKean, Fourier series and integrals. Probability and Mathematical Statistics, No. 14. Academic Press, New York-London, 1972. Search in Google Scholar

[7] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimees sous elliptiques sur certains groupes nilpotents. Acta Math. 139 (1977), 95–153. Search in Google Scholar

[8] P. Hajłasz, Sobolev spaces on metric-measure spaces, in Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002), 173–218, Contemp. Math., 338, Amer. Math. Soc., Providence, RI, 2003. 10.1090/conm/338/06074Search in Google Scholar

[9] A. Hurwitz, Sur quelques applications géométriques des séries de Fourier, Ann. Ecole Norm. Sup. 19 (1902) 357–408. 10.24033/asens.514Search in Google Scholar

[10] S. G. Krantz, H. R. Parks, A primer of real analytic functions. Second edition. Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser Boston, Inc., Boston, MA, 2002. Search in Google Scholar

[11] R. Montgomery, A tour of subriemannian geometries, their geodesics and applications. Mathematical Surveys and Monographs, 91. American Mathematical Society, Providence, RI, 2002. Search in Google Scholar

[12] R. Monti, Distances, boundaries and surface measures in Carnot-Carathéodory spaces, PhD thesis 2001. Available at http: //www.math.unipd.it/~monti/PAPERS/TesiFinale.pdf 10.1007/s005260000076Search in Google Scholar

[13] R. Monti, Some properties of Carnot-Carathéodory balls in the Heisenberg group, Rend. MatA˙ cc. Lincei 11 (2000) 155–167. Search in Google Scholar

[14] I. J. Schoenberg, An isoperimetric inequality for closed curves convex in even-dimensional Euclidean spaces. Acta Math. 91 (1954), 143–164. Search in Google Scholar