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Plurisubharmonic Functions on the Octonionic Plane and Spin(9)-Invariant Valuations on Convex Sets

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Abstract

A new class of plurisubharmonic functions on the octonionic plane \(\mathbb{O}^{2}\simeq\mathbb{R}^{16}\) is introduced. An octonionic version of theorems of A.D. Aleksandrov (Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 13(1):5–24, 1958) and Chern-Levine-Nirenberg (Global Analysis, pp. 119–139, 1969), and Błocki (Proc. Am. Math. Soc. 128(12):3595–3599, 2000) are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of \(\mathbb{O}^{2}\simeq\mathbb{R}^{16}\) . In particular, a new example of Spin(9)-invariant valuation on ℝ16 is given.

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  1. Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Semyon Alesker

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  1. Semyon Alesker
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Correspondence to Semyon Alesker.

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Partially supported by ISF grant 1369/04.

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Alesker, S. Plurisubharmonic Functions on the Octonionic Plane and Spin(9)-Invariant Valuations on Convex Sets. J Geom Anal 18, 651–686 (2008). https://doi.org/10.1007/s12220-008-9032-0

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  • DOI: https://doi.org/10.1007/s12220-008-9032-0

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