Regular multi-types and the Bloom conjecture

Xiaojun Huang; Wanke Yin

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arXiv · 1902.10581

Regular multi-types and the Bloom conjecture

Xiaojun Huang·Wanke Yin

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Abstract

We prove equality of the vector field (iterated commutator) type and the regular contact type, which together with the Bloom theorem on equality of the Levi-form type and the regular contact type provides a complete solution of a long standing open problem of Bloom in the case of complex dimension three. For general dimensions, we verify the Bloom conjecture when $s=n-2$, which provides the first positive result in the pseudoconvexity sensitive case for a real hypersurface in ${\mathbb{C}}^n$ after his important work in 1981.

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Xiaojun Huang, Wanke Yin. 2019-02-27. Regular multi-types and the Bloom conjecture. https://arxiv.org/abs/1902.10581

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