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Convex floating bodies as approximations of Bergman sublevel sets on tube domains


Author: Purvi Gupta
Journal: Proc. Amer. Math. Soc. 145 (2017), 4385-4396
MSC (2010): Primary 32A07, 32A25, 52A23
DOI: https://doi.org/10.1090/proc/13573
Published electronically: April 28, 2017
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Abstract: For a pseudoconvex tube domain, we prove estimates that relate the sublevel sets of its diagonal Bergman kernel to the floating bodies of its convex base. This allows us to associate a new affine invariant to any convex body.


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Additional Information

Purvi Gupta
Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
Email: pgupta45@uwo.ca

DOI: https://doi.org/10.1090/proc/13573
Keywords: Tube domains, floating body, equiaffine invariant measures
Received by editor(s): April 18, 2016
Received by editor(s) in revised form: November 6, 2016
Published electronically: April 28, 2017
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society