Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group ℍ n
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Balogh, Z.M. Size of characteristic sets and functions with prescribed gradient,J. Reine Angew. Math. 564, 63–83, (2003).
Barbosa, J.L., do Carmo, M., and Eschenburg, J. Stability of hypersurfaces of constant mean curvature in Riemannian manifolds,Math. Z. 197(1), 123–138, (1988).
Bonk, M. and Capogna, L. Horizontal mean curvature flow in the Heisenberg group, in preparation.
Capogna, L., Danielli, D., and Garofalo, N. An isoperimetric inequality and the geometric Sobolev embedding for vector fields,Math. Res. Lett. 1(2), 203–215, (1994).
Cheng, J.-H. and Hwang, J.-F. Properly embedded and immersed minimal surfaces in the Heisenberg group,Bull. Austral. Math. Soc. 70(3), 507–520, (2004).
Cheng, J.-H., Hwang, J.-F., Malchiodi, A., and Yang, P. Minimal surfaces in pseudohermitian geometry,Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4(1), 129–177, (2005).
Cheng, J.-H., Hwang, J.-F., and Yang, P. Existence and uniqueness for p-area minimizers in the Heisenberg group, arXiv:math.DG/0601208.
Danielli, D., Garofalo, N., andNhieu, D.-M. Minimal surfaces, surfaces of constant mean curvature and isoperimetry in sub-Riemannian groups, preprint, (2004).
Delaunay, C. Sur la surface of revolution dont la courbure moyenne est constante,J. Math. Pure Appl. 16, 309–321, (1841).
Figueroa, C.B., Mercuri, F., and Pedrosa, R.N.L. Invariant surfaces of the Heisenberg groups,Ann. Mat. Pura Appl. (4) 177, 173–194, (1999).
Franchi, B., Serapioni, R.,and Serra Cassano, F. Rectifiability and perimeter in the Heisenberg group,Math. Ann. 321(3), 479–531, (2001).
Garofalo, N. and Pauls, S. The Bernstein problem in the Heisenberg group, preprint, (2004).
Giaquinta, M. and Hildebrandt, S.Calculus of Variations I, II, Grundlehren der Mathematischen Wissenschaften,310, 311, Springer-Verlag, Berlin, (1996).
Gromov, M.Structures Métriques pour les Variétés Riemanniennes, Vol. 1 of Textes Mathématiques, CEDIC, Paris, (1981).
Gromov, M. Camot-Carathéodory spaces seen from within sub-riemannian geometry,Prog. Math. 144, Birkhäuser, Basel, 79–323, (1996).
Hladky, R.K. and Pauls, S. Constant mean curvature surfaces in sub-Riemannian geometry, arXiv:math.DG/059636.
Hsiang, W.-Y. On generalization of theorems of A.D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature,Duke Math. J. 49(3), 485–496, (1982).
Korevaar, N.J., Kusner, R., and Solomon, B. The structure of complete embedded surfaces with constant mean curvature,J. Differential Geom. 30(2), 465–503, (1989).
Leonardi, G.P. and Masnou, S. On the isoperimetric problem in the Heisenberg group ℍn,Ann. Mat. Pura Appl. (4) 184(4), 533–553, (2005).
Leonardi, G.P. and Rigot, S. Isoperimetric sets on Carnot groups,Houston J. Math. 29(3), 609–637, (electronic), (2003).
Monti, R. Brunn-Minkowski and isoperimetric inequality in the Heisenberg group,Ann. Acad. Sci. Fenn. Math. 28(1), 99–109, (2003).
Monti, R. and Serra Cassano, F. Surface measures in Carnot-Carathéodory spaces,Calc. Van 13, 339–376, (2001).
Ni, Y. Sub-Riemannian constant mean curvature surfaces in the Heisenberg group as limits,Ann. Mat. Pura Appl. (4) 183(4), 555–570, (2004).
Pansu, P. Une inégalité isopérimétrique sur le groupe de Heisenberg,C.R. Acad. Sci. Paris Sér. I Math. 295(2), 127–130, (1982).
Pansu, P. An isoperimetric inequality on the Heisenberg group,Rend. Sem. Mat. Univ. Politec. Torino Special Issue (1983), 159–174, Conference on differential geometry on homogeneous spaces (Turin, 1983), (1984).
Pansu, P. Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un,Ann. of Math. (2) 129(1), 1–60, (1989).