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arXiv · 0707.4385

Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets

Semyon Alesker
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Abstract

A new class of plurisubharmonic functions on the octonionic plane O^2= R^{16} is introduced. An octonionic version of theorems of A.D. Aleksandrov and Chern- Levine-Nirenberg, and Blocki are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of O^2=R^{16}. In particular a new example of Spin(9)-invariant valuation on R^{16} is given.

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Semyon Alesker. 2016-07-26. Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets. https://arxiv.org/abs/0707.4385

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