Minimal surfaces over Carnot manifolds

M. B. Karmanova

Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 74-101.

Résumé

We consider minimal graph-surfaces constructed from contact mappings of Carnot manifolds with values in Carnot-Carathéodory spaces. We establish basic properties of these graph-surfaces and distinguish the case in which the image space is endowed with the structure of a group. It turns out that, in the non-holonomic case, the problem is well posed if certain requirements on the preimage are satisfied. We find these requirements. One of auxiliary results provides us with an explicit form of the area formula for the graph constructed from a contact mapping.

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