On the boundary complex of the k-Cauchy–Fueter complex
On the boundary complex of the k-Cauchy–Fueter complex
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DOI：
10.1007/s10231-023-01319-w
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发表时间：
2022-10
期刊：
影响因子：
--
通讯作者：
Wei Wang
中科院分区：
文献类型：
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作者：
Wei Wang
Thek-Cauchy–Fueter complex,, in quaternionic analysis are the counterpart of the Dolbeault complex in the theory of several complex variables. In this paper, we construct explicitly boundary complexes of these complexes on boundaries of domains, corresponding to the tangential Cauchy–Riemann complex in complex analysis. They are only known boundary complexes outside of complex analysis that have interesting applications to the function theory. As an application, we establish the Hartogs–Bochner extension fork-regular functions, the quaternionic counterpart of holomorphic functions. These boundary complexes have a very simple form on a kind of quadratic hypersurfaces, which have the structure of right-type nilpotent Lie groups of step two. They allow us to introduce the quaternionic Monge–Ampère operator and open the door to investigate pluripotential theory on such groups. We also apply abstract duality theorem to boundary complexes to obtain the generalization of Malgrange’s vanishing theorem and the Hartogs–Bochner extension fork-CF functions, the quaternionic counterpart of CR functions, on this kind of groups.
