# A new generalization of the Lelong number Licentiatavhandling, 2009

We will introduce a quantity which measures the singularity of a plurisubharmonic function $\varphi$ relative to another plurisubharmonic function $\psi$, at a point $a$. We denote this quantity by $\nu_{a,\psi}(\varphi)$. It can be seen as a generalization of the classical Lelong number in a natural way: if $\psi=(n-1)\log| \cdot - a|$ where $n$ is the dimension of the set where $\varphi$ is defined, then $\nu_{a,\psi}(\varphi)$ coincides with the classical Lelong number of $\varphi$ at the point $a$. The main theorem of this thesis says that the upper level sets of our generalized Lelong number, i.e. the sets of the form $\{z: \nu_{z,\psi}(\varphi) \geq c \}$ where $c>0$, are in fact analytic sets, provided that the \textit{weight} $\psi$ satisfies some additional conditions.
Euler
Opponent: Mikael Passare

## Författare

#### Aron Lagerberg

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

#### Ämneskategorier

Matematisk analys

Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University

Euler

Opponent: Mikael Passare

2017-10-07