Local growth of pluri-subharmonic functions
Abstract
We obtain two-bound estimates for the local growth of pluri-subharmonic functions in terms of Siciak and relative extremal functions. As applications, we give simple new proofs of "Bernstein doubling inequality" and the main result in [Alexander Brudnyi, Local inequalities for pluri-subharmonic functions, Annals Math. 149 (1999), No. 2, pp. 511--533]. We propose a conjecture similar to the comparison theorem in [H. Alexander and B. A. Taylor, Comparison of two capacities in , Math. Z. 186 (1984), 407--417], whose validity allows to obtain bounds for the local growth of pluri-subharmonic functions solely in term of the Siciak extremal functions.
Keywords
Cite
@article{arxiv.0908.4355,
title = {Local growth of pluri-subharmonic functions},
author = {Tuyen Trung Truong},
journal= {arXiv preprint arXiv:0908.4355},
year = {2009}
}
Comments
Complete arguments to new proofs of the main result in Brudnyi's paper and to the "Berstein doubling inequality" are added. Several other changes/corrections. 8 pages