Plurisubharmonic Functions on the Octonionic Plane and <Emphasis Type="Italic">Spin</Emphasis>(9)-Invariant Valuations on Convex Sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Plurisubharmonic Functions on the Octonionic Plane and <Emphasis Type="Italic">Spin</Emphasis>(9)-Invariant Valuations on Convex Sets

Authors:	Semyon Alesker

Institution:	(1) Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel

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. Partially supported by ISF grant 1369/04.

Keywords:	Plurisubharmonic functions Convex sets Valuations Octonions
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