Work

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

Year: 2026

Type: article

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 $$\mathbb {C}^{10}$$ 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.

Source: Complex Analysis and its Synergies

DOI: 10.1007/s40627-026-00212-5

Authors: Florian Bertrand, Martin Kolář, Francine Meylan

Institutions: American University of Beirut, Masaryk University, University of Fribourg

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Grantová Agentura České Republiky