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1. CMB 2011 (vol 55 pp. 242)
Convergence in Capacity In this note we study the convergence of sequences of Monge-AmpÃ¨re measures $\{(dd^cu_s)^n\}$,
where $\{u_s\}$ is a given sequence of plurisubharmonic functions, converging in capacity.
Keywords:complex Monge-AmpÃ¨re operator, convergence in capacity, plurisubharmonic function Categories:32U20, 31C15 |
2. CMB 2004 (vol 47 pp. 481)
A New Characterization of Hardy Martingale Cotype Space We give a new characterization of Hardy martingale cotype
property of complex quasi-Banach space by using the existence of a
kind of plurisubharmonic functions. We also characterize the best
constants of Hardy martingale inequalities with values
in the complex quasi-Banach space.
Keywords:Hardy martingale, Hardy martingale cotype,, plurisubharmonic function Categories:46B20, 52A07, 60G44 |
3. CMB 2003 (vol 46 pp. 373)
Potential Theory of the Farthest-Point Distance Function We study the farthest-point distance function, which measures the
distance from $z \in \mathbb{C}$ to the farthest point or points of
a given compact set $E$ in the plane.
The logarithm of this distance is subharmonic as a function of $z$,
and equals the logarithmic potential of a unique probability measure
with unbounded support. This measure $\sigma_E$ has many interesting
properties that reflect the topology and geometry of the compact set
$E$. We prove $\sigma_E(E) \leq \frac12$ for polygons inscribed in a
circle, with equality if and only if $E$ is a regular $n$-gon for some
odd $n$. Also we show $\sigma_E(E) = \frac12$ for smooth convex sets of
constant width. We conjecture $\sigma_E(E) \leq \frac12$ for all~$E$.
Keywords:distance function, farthest points, subharmonic function, representing measure, convex bodies of constant width Categories:31A05, 52A10, 52A40 |