9
votes
1answer
534 views

An exponential polynomial with at least one bounded positivity component

In a forthcoming paper on nodal domains of Gaussian random functions, we (I and Misha Sodin) have a statement that is, roughly speaking, the following: if bounded nodal domains are possible at all, ...
14
votes
2answers
583 views

Curve integral of exponent of superharmonic function.

Let $\phi$ be a real smooth superharmonic function on unit disc $D$ in $\mathbb C$; i.e. $\triangle \phi\le 0$. Then there is a curve $\gamma$ from the center of $D$ to its boundary such that ...