TY - JOUR
T1 - Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets
AU - Alesker, Semyon
N1 - Funding Information:
Partially supported by ISF grant 1369/04.
PY - 2008/7
Y1 - 2008/7
N2 - A new class of plurisubharmonic functions on the octonionic plane double-struck O sign 2≃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 double-struck O sign 2≃ℝ 16. In particular, a new example of Spin(9)-invariant valuation on ℝ 16 is given.
AB - A new class of plurisubharmonic functions on the octonionic plane double-struck O sign 2≃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 double-struck O sign 2≃ℝ 16. In particular, a new example of Spin(9)-invariant valuation on ℝ 16 is given.
KW - Convex sets
KW - Octonions
KW - Plurisubharmonic functions
KW - Valuations
UR - http://www.scopus.com/inward/record.url?scp=84867942245&partnerID=8YFLogxK
U2 - 10.1007/s12220-008-9032-0
DO - 10.1007/s12220-008-9032-0
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AN - SCOPUS:84867942245
SN - 1050-6926
VL - 18
SP - 651
EP - 686
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -