arXiv subjects
Publications and source records attributed to Dau Hoang Hung.
We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to oscillatory integrals and integration indices of real polynomial are also given.
Let $D$ be a bounded domain in $\mathbb C^n$. We study approximation of (not necessarily bounded from above) $m-$subharmonic function $D$ by continuous $m-$subharmonic ones defined on neighborhoods of $\overline{D}$. We also consider the existence of a $m-$subharmonic function on $D$ whose boundary values coincides with a given real valued continuous function on $\partial D$ except for a sufficiently small subset of $\partial D.$