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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Quaternionic plurisubharmonic functions and their applications to convexity


Author: S. Alesker
Original publication: Algebra i Analiz, tom 19 (2007), nomer 1.
Journal: St. Petersburg Math. J. 19 (2008), 1-13
MSC (2000): Primary 31C10, 52A38, 52A39
Published electronically: December 12, 2007
MathSciNet review: 2319507
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Abstract: The paper is a survey of the recent theory of plurisubharmonic functions of quaternionic variables, together with its applications to the theory of valuations on convex sets and HKT-geometry (Hyper-Kähler with Torsion). The exposition follows some earlier papers by the author and a joint paper by Verbitsky and the author.


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Additional Information

S. Alesker
Affiliation: Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
Email: semyon@post.tau.ac.il

DOI: https://doi.org/10.1090/S1061-0022-07-00982-X
Keywords: HKT-geometry, valuation on convex sets, quaternionic plurisubharmonic functions
Received by editor(s): August 1, 2006
Published electronically: December 12, 2007
Additional Notes: Partially supported by ISF (grant 1369/04)
Dedicated: Dedicated to Professor Victor Abramovich Zalgaller on the occasion of his 85th birthday
Article copyright: © Copyright 2007 American Mathematical Society