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arXiv · 2506.21221

New examples of CR submanifolds for the $2$-jet determination problem

Florian Bertrand·Martin Kolář·Francine Meylan
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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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Florian Bertrand, Martin Kolář, Francine Meylan. 2025-06-26. New examples of CR submanifolds for the $2$-jet determination problem. https://arxiv.org/abs/2506.21221

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