Monogenic hull for the n-Cauchy-Fueter operator and twistor theory

2018/06/18 by Tomáš Salač, Salac, Tomas
Mathematics · #32L25 #35N05 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1806.06797

openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first part in a series of three articles in which are studied the domains of monogenicity for the n-Cauchy-Fueter operator. Using the twistor theory, we will in this article show that for a given open subset U of ℚⁿ, there is an open subset H(U), called the monogenic hull of U, of M_{2n× 2}^ℂ=ℚⁿ⊗ℂ such that each monogenic function in U extends to a unique pair of holomorphic functions on H(U). In the second part of the series we will exploit the twistor theory furthermore to prove that any pseudoconvex domain in ℚⁿ is a domain of monogenicity. In the third part of the series, we show the other implication and provide a geometric characterization of the domains of monogenicity.

Related

• Twistor theory and the harmonic hull
• Fueter's theorem for monogenic functions in biaxial symmetric domains
• The Fueter-Sce mapping and the Clifford-Appell polynomials
• Biaxial monogenic functions from Funk-Hecke's formula combined with Fueter's theorem
• Further Aspects of the Fueter Mapping Theorem