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A new generalization of the Lelong number

Aron Lagerberg (Institutionen för matematiska vetenskaper, matematik)
Göteborg : Chalmers University of Technology, 2009. - 38 s.
[Licentiatavhandling]

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.



Denna post skapades 2010-11-02. Senast ändrad 2010-11-19.
CPL Pubid: 128512

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys

Chalmers infrastruktur

Examination

Datum: 2009-05-29
Tid: 13:15
Lokal: Euler
Opponent: Mikael Passare

Ingår i serie

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