On the Nonexistence of a Hypersurface of Prescribed Mean Curvature with a Given Boundary.
Plane -webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two -webs, are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable -webs, however, there always exists a nonmeasurable conjugacy; still,...