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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {C}^{10}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>10</mn> </msup> </math></EquationSource> </InlineEquation> that is not strictly pseudoconvex and for which its germs of CR automorphisms are determined by their 2-jets at a given point.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • Florian Bertrand,
  • Martin Kolář,
  • Francine Meylan

摘要

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.