Metric normal and distance function in the Heisenberg group

Mathematische Zeitschrift

Volumn 256, Issue 3, 2007, Pages 661-684

  Arcozzi, Nicola ^a   Ferrari, Fausto ^a,b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b CIRAM   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247373032     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-006-0098-8     Document Type: Article

References (18)

1. Albano, P., Bove, A.: Analytic stratifications and the cut locus of a class of distance functions. Israel J. Math. 154, 61-91 (2006)
2. Arcozzi, N., Ferrari, F.: The Hessian of the distance from a surface in the Heisenberg group, preprint (2004)
3. Arcozzi, N., Morbidelli, D.: Stability of isometric maps in the Heisenberg group, preprint (2005)
4. Bellaïche, A.: The tangent space in sub-Riemannian geometry. In: Bellaiche Risler, J. (eds.) Sub-Riemannian Geometry Progress In Mathematics, Vol. 144, pp. 1-78. Birkhauser, Basel (1996)
5. Delfour, M.C., Zolésio, J.-P.: Oriented distance function and its evolution equation for initial sets with thin boundary. SIAM J. Control. Optim. 42(6), 2286-2304 (2004)
6. Federer, H.: Curvature measures. Trans. Amer. Math. Soc. 93, 418-491 (1959)
7. Franchi, B., Serapioni, R., Serra Cassano, F.: Rectifiability and perimeter in the Heisenberg group. Math. Ann. 321, 479-531 (2001)
8. Gromov, M: Carnot-Charathéodory spaces seen from within. In: Bellaiche, Risler, J. (eds.) Sub-Riemannian Geometry Progress InMathematics, Vol. 144, pp. 79-318. Birkhauser, Basel (1996)
9. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. 2nd edn. Springer, Berlin Heidelberg New York (1983)
10. k hypersurfaces. J. Differential Equations 40((1), 116-120 (1981)
11. Montgomery, R.: A tour of subriemannian geometries. their geodesies and applications. Mathematical Surveys and Monographs, Vol. 91, xx+259 pp. American Mathematical Society, Providence, RI (2002)
12. Monti, R.: Some properties of Carnot-Carathéodory balls in the Heisenberg group. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl. 11. 3(9), 155-167 (2001)
13. Monti, R., Serra Cassano, F.: Surface measures in Carnot- Carathéodory spaces. Calc. Var. Partial Differential Equations 13(3), 339-376 (2001)
14. Nagel, A., Stein, E.M., Wainger, S.: Balls and metrics defined by vector fields I: basic properties. Acta Math. 155, 103-147 (1985)
15. Pansu, P.: Une inégalité isoperimetrique sur le groupe de Heisenberg. C.R. Acad. Sc. Paris, Série I. 295, 127-130 (1982)
16. Pansu, P.: Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. of Math. 129, 1-60 (1989)
17. Spanier, E.H.: Algebraic topology. Corrected reprint. Springer, Berlin Heidelberg New York (1981)
18. Stein, E.M.: Harmonic Analysis: Real variable methods, orthogonality and oscillatory integrals. Princeton University Press, Princeton (1993)