Unique jet determination of CR maps into Nash sets
<p dir="ltr">Let M ⊂ C<sup>N</sup> be a real-analytic CR submanifold, M′ ⊂ C<sup>N′ </sup>a Nash set and <sup>E</sup>M′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p ∈ M , and for ever...
محفوظ في:
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2023
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إضافة وسم
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| الملخص: | <p dir="ltr">Let M ⊂ C<sup>N</sup> be a real-analytic CR submanifold, M′ ⊂ C<sup>N′ </sup>a Nash set and <sup>E</sup>M′ the set of points in M′ of D'Angelo infinite type. We show that if M is minimal, then, for every point p ∈ M , and for every pair of germs of C<sup>∞</sup> -smooth CR maps f , g : ( M , p ) → M′ , there exists an integer k = k<sub>p</sub> such that if f and g have the same k-jets at p, and do not send M into E M′ , then necessarily f = g . Furthermore, the map p ↦ k p may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in C <sup>N</sup> into Nash subsets in C<sup>N′ </sup>of D'Angelo finite type, for arbitrary N , N′ ≥ 2.</p><h2>Other Information</h2><p dir="ltr">Published in: Advances in Mathematics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.aim.2023.109271" target="_blank">https://dx.doi.org/10.1016/j.aim.2023.109271</a></p> |
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