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New examples of CR submanifolds for the $2$-jet determination problem (2506.21221v1)

Published 26 Jun 2025 in math.CV

Abstract: This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the $2$-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in light of those, we formulate a general problem and illustrate it with examples. In the second part of the paper, we provide a new example of a real submanifold of codimension $7$ in $\mathbb{C}{10}$ that is not strictly pseudoconvex and for which its germs of CR automorphisms are determined by their $2$-jets at a given point.

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