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arXiv · 1809.03748

The tangential $k$-Cauchy-Fueter complexes and Hartogs' phenomenon over the right quaternionic Heisenberg group

Yun Shi·Wei Wang
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Abstract

We construct the tangential $k$-Cauchy-Fueter complexes on the right quaternionic Heisenberg group, as the quaternionic counterpart of $\overline{\partial}_b$-complex on the Heisenberg group in the theory of several complex variables. We can use the $L^2$ estimate to solve the nonhomogeneous tangential $k$-Cauchy-Fueter equation under the compatibility condition over this group modulo a lattice. This solution has an important vanishing property when the group is higher dimensional. It allows us to prove the Hartogs' extension phenomenon for $k$-CF functions, which are the quaternionic counterpart of CR functions.

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Yun Shi, Wei Wang. 2018-09-11. The tangential $k$-Cauchy-Fueter complexes and Hartogs' phenomenon over the right quaternionic Heisenberg group. https://arxiv.org/abs/1809.03748

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