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
Abstract: We show that in every bounded convex domain in there exists a smooth convex exhaustion function such that the product of all eigenvalues of the matrix is . Moreover, if the domain is strictly convex, then can be chosen so that every eigenvalue is .
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