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

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

2007-07-30

arxiv.org/abs/0707.4385v3

J. Geom. Anal. 18 (2008), no. 3, 651--686

Mathematics

Metric Geometry

35 pages, minor corrections, references

Scientific paper

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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