The complex equilibrium measure of a symmetric convex set in
Authors:
Eric Bedford and B. A. Taylor
Journal:
Trans. Amer. Math. Soc. 294 (1986), 705-717
MSC:
Primary 32F05; Secondary 31C10
DOI:
https://doi.org/10.1090/S0002-9947-1986-0825731-8
MathSciNet review:
825731
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Abstract | References | Similar Articles | Additional Information
Abstract: We give a formula for the measure on a convex symmetric set in
which is the Monge-Ampere operator applied to the extremal plurisubharmonic function
for the convex set. The measure is concentrated on the set
and is absolutely continuous with respect to Lebesgue measure with a density which behaves at the boundary like the reciprocal of the square root of the distance to the boundary. The precise asymptotic formula for
near a boundary point
of
is shown to be of the form
, where the constant
depends both on the curvature of
at
and on the global structure of
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0825731-8
Keywords:
Plurisubharmonic function,
Monge-Ampere operator,
extremal function
Article copyright:
© Copyright 1986
American Mathematical Society