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...4 it is still unknown if similar examples can be obtained. We would like to mention that examples of area-minimizing surfaces in H 1 with low Euclidean regularity have been obtained in [11], [31] and =-=[29]-=-. Hence our results are optimal in the class of C 2 area-stationary surfaces. Finally, the techniques in this paper can be employed to prove classification results for complete stable area-stationary ...

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...e here is St(u) on page 16 of [32]. Also the boundary value in [32] is more general (see previous comments after Theorem A for more details). Added in proof: The authors were informed of papers [18], =-=[24]-=- in which the second variation of the p-area was also studied and discussed. Acknowledgments The first author’s research was supported in part by NSC 97-2115-M001-016-MY3. He would also like to thank ...

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...ndaries of the conjectured solutions to the isoperimetric problem are of class C2, see [11], although there exist examples of area-minimizing horizontal graphs which are just Euclidean lipschitz, see =-=[16, 35, 39]-=-. Cheng, Hwang and Yang [16, Thms. A, B] proved existence and uniqueness of t-graphs which are Lipschitz continuous solutions of the minimal surface equation in Hn under given Dirichlet conditions in ...

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...es, we shall refer the reader to [2], [5], [6], [12], [38, 39, 40, 41, 42], [27, 28, 29], [44], [43], [58, 59], [67, 68], [55], [7]. We would also like to quote [21], [44], [77], [78], [13, 14], [8], =-=[71]-=-, for some recent results about minimal and constant mean-curvature hypersurfaces immersed in the Heisenberg group. In this paper we shall try to give some contribution to the study of both analytic a...

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...-Riemannian 3-manifold. Second variation formulas for the area have appeared in different contexts. In the first Heisenberg group M(0) such formulas have been proved for minimal intrinsic graphs [4], =-=[41]-=-, [49], and for any minimal surface [19], [35]. In [15] and [32], second variation formulas are obtained for variations of class C3 of CMC surfaces in pseudo-Hermitian 3-manifolds and in vertically ri...