Pizzetti and Cauchy formulae for higher dimensional surfaces: Adistributional approach

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Adan, Ali Guzman¹  Sommen, Frank¹ 

[1] Univ Ghent, Clifford Res Grp, Dept Math Anal, Fac Engn & Architecture, Krijgslaan 281, B-9000 Ghent, Belgium

关键词: Pizzetti formula;    Cauchy theorem;    Integration;    Distributions;    Manifolds;    Dirac operator;   

DOI  :  10.1016/j.jmaa.2020.124140

来源: Elsevier

【 摘 要 】

In this paper, we study Pizzetti-type formulas for Stiefel manifolds and Cauchy-type formulas for the tangential Dirac operator from a distributional perspective. First we illustrate a general distributional method for integration over manifolds in R-m defined by means of kequations phi(1)((x) under bar) = ... = phi(k)((x) under bar) = 0. Next, we apply this method to derive an alternative proof of the Pizzetti formulae for the real Stiefel manifolds SO(m)/SO(m - k). Besides, a distributional interpretation of invariant oriented integration is provided. In particular, we obtain a distributional Cauchy theorem for the tangential Dirac operator on an embedded (m - k)-dimensional smooth surface. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free