Divergence theorems and the supersphere

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• 作者：Josua Groeger
• 关键词：Semi-Riemannian supergeometry ; Divergence theorems ; Supersphere ; Mean value theorems
• 刊名：Journal of Geometry and Physics
• 出版年：March, 2014
• 年：2014
• 卷：77
• 期：Complete
• 页码：13-29
• 全文大小：486 K

文摘

The transformation formula of the Berezin integral holds, in the non-compact case, only up to boundary integrals, which have recently been quantified by Alldridge-Hilgert-Palzer. We establish divergence theorems in semi-Riemannian supergeometry by means of the flow of vector fields and these boundary integrals, and show how superharmonic functions are related to conserved quantities. An integration over the supersphere was introduced by Coulembier-De Bie-Sommen as a generalisation of the Pizzetti integral. In this context, a mean value theorem for harmonic superfunctions was established. We formulate this integration along the lines of the general theory and give a superior proof of two mean value theorems based on our divergence theorem.