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Smooth exhaustion functions in convex domains

Author: Zbigniew Blocki
Journal: Proc. Amer. Math. Soc. 125 (1997), 477-484
MSC (1991): Primary 26B25; Secondary 35J60
MathSciNet review: 1350934
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Abstract: We show that in every bounded convex domain in $\mathbb R^n$ there exists a smooth convex exhaustion function $\psi $ such that the product of all eigenvalues of the matrix $(\partial ^2\psi /\partial x_j\partial x_k)$ is $\ge 1$. Moreover, if the domain is strictly convex, then $\psi $ can be chosen so that every eigenvalue is $\ge 1$.

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Zbigniew Blocki
Affiliation: Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland

Received by editor(s): March 27, 1995
Received by editor(s) in revised form: August 14, 1995
Additional Notes: The author was partially supported by KBN Grant No. 2 PO3A 058 09.
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1997 American Mathematical Society

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