In the Heisenberg group H^1 with a sub-Finsler structure, an (X,Y)-Lipschitz surface which is complete, oriented, connected and stable must be a vertical plane. In particular, the result holds for entire intrinsic graphs of Euclidean Lipschitz functions.
The Bernstein problem for (X,Y )-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups / Giovannardi, Gianmarco; Ritoré, Manuel. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - ELETTRONICO. - ..:(2024), pp. 0-0. [10.1142/S0219199723500487]
The Bernstein problem for (X,Y )-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups
Giovannardi, Gianmarco
;
2024
Abstract
In the Heisenberg group H^1 with a sub-Finsler structure, an (X,Y)-Lipschitz surface which is complete, oriented, connected and stable must be a vertical plane. In particular, the result holds for entire intrinsic graphs of Euclidean Lipschitz functions.
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