One dimensional symmetry in the Heisenberg group
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 269-284. 
@article{ASNSP_2001_4_30_2_269_0,
     author = {Birindelli, Isabeau and Prajapat, Jyotshana},
     title = {One dimensional symmetry in the {Heisenberg} group},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {269--284},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {2},
     year = {2001},
     mrnumber = {1895712},
     zbl = {1014.35019},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_2001_4_30_2_269_0/}
}
TY  - JOUR
AU  - Birindelli, Isabeau
AU  - Prajapat, Jyotshana
TI  - One dimensional symmetry in the Heisenberg group
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2001
SP  - 269
EP  - 284
VL  - 30
IS  - 2
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_2001_4_30_2_269_0/
LA  - en
ID  - ASNSP_2001_4_30_2_269_0
ER  - 
%0 Journal Article
%A Birindelli, Isabeau
%A Prajapat, Jyotshana
%T One dimensional symmetry in the Heisenberg group
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2001
%P 269-284
%V 30
%N 2
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_2001_4_30_2_269_0/
%G en
%F ASNSP_2001_4_30_2_269_0
Birindelli, Isabeau; Prajapat, Jyotshana. One dimensional symmetry in the Heisenberg group. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 269-284. http://archive.numdam.org/item/ASNSP_2001_4_30_2_269_0/

[1] L. Ambrosio - X. Cabré, Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (2000), 725-739. | MR | Zbl

[2] M.T. Barlow - R.F. Bass - C. Gui, The Liouville property and a conjecture of De Giorgi, Comm. Pure Appl. Math. 53 (2000), 1007-1038. | MR | Zbl

[3] H. Berestycki - L. Caffarelli - L. Nirenberg, Monotonicity for elliptic equations in unbounded domains, Comm. Pure Appl. Math. 50 (1997), 1088-1111. | MR | Zbl

[4] H. Berestycki - F. Hamel - R. Monneau, One-dimensional symmetry of bounded entire solutions of some elliptic equations, Duke Math. J. 103 (2000), 375-396. | MR | Zbl

[5] H. Berestycki - L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat. 22 (1991), 1-37. | MR | Zbl

[6] H. Berestycki - L. Nirenberg - S.R.S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operator in general domains, Comm. Pure Appl. Math. (1994), 47-92. | MR | Zbl

[7] I. Birindelli, Hopf's lemma and anti-maximum principle in general domains, J. Differential Equations 119 (1995), 450-472. | MR | Zbl

[8] I. Birindelli, Superharmonic functions in the Heisenberg group: estimates and Liouville theorems, to appear in NoDEA. | MR | Zbl

[9] I. Birindelli - J. Prajapat, Nonlinear Liouville theorems in the Heisenberg group via the moving plane method, Comm. Partial Differential Equations 24 (1999), 1875-1890. | MR | Zbl

[10] I. Birindelli - J. Prajapat, Monotonicity results for nilpotent stratified groups, Pacific J. Math., to appear. | MR

[11] A. Farina, Symmetry for solutions of semilinear elliptic equations in RN and related conjectures, Ricerche di Matematica 48 (1999), 129-154. | MR | Zbl

[12] E. De Giorgi, Convergence problems for functionals and operators, Proc. Int. Meeting on Recent Methods in Nonlinear Analysis (Rome 1978), Pitagora (ed.), Bologna (1979), pp. 131-188. | MR | Zbl

[13] N. Ghoussoub - C. Gui, On a conjecture of De Giorgi and some related problems, Math. Ann. 311 (1998), 481-491. | MR | Zbl

[14] D.S. Jerison, Boundary regularity in the Dirichlet problem for □b on CR manifolds, Comm. Pure Appl. Math. 36 (1983), 143-181. | Zbl

[15] D.S. Jerison, The Poincaré inequality for vector fields satisfying Hörmander's condition, Duke Math. J. 53 (1986), 503-523. | MR | Zbl

[16] D.S. Jerison, A. Sánchez-Calle, Subelliptic, second order differential operators, Complex analysis, III (College Park, Md., 1985-86), 46-77, Lecture Notes in Math., 1277, Springer, Berlin-New York, 1987. | MR | Zbl

[17] Kohn - L. Nirenberg, Non coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. | MR | Zbl

[18] E.A. Stein, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals", Princeton Mathematical Series, 43, 1993. | MR | Zbl

[19] N. Varopoulos - L. Saloff-Coste - T. Coulhon, "Analysis and geometry on groups, Cambridge tracts in Mathematics 100", Cambridge University Press, 1992. | MR | Zbl