GREEN FUNCTIONS WITH SINGULARITIES ALONG COMPLEX SPACES
By A. Rashkovskii, R. Sigurdsson. 2004
48 citations recorded by the source corpus.
We study properties of a Green function GA with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u≤ log |ψ|+C, where ψ=(ψ1,…,ψm), ψ1,…,ψm are local generators for the ideal sheaf ℐA of A, and C is a constant depending on the function u and the generators. A motivation for this study is to estimate global bounded functions from the sheaf ℐA and thus proving a "Schwarz lemma" for ℐA.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/67637a340754dc2ce9073014141e28f5050cd8de
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In Applied Mathematics
- Chinh H. Lu
- Tam'as Darvas
- E. Di Nezza
- Chi Li
- Jingrui Cheng
- Xiuxiong Chen
- Robert J. Berman
- Giovanni Molica Bisci
In Geometry and Topology
- Chinh H. Lu
- Tam'as Darvas
- E. Di Nezza
- Chi Li
- Jingrui Cheng
- Xiuxiong Chen
- Robert J. Berman
- B. Berndtsson
Citations in the corpus
- Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity (2017, background): “odel type singularity. • All analytic singularity types (those that can be locally written as clog P j|fj| 2 +g, where fjare holomorphic, c>0 and gis smooth) are of model type ([RWN1, Remark 4.6], [RS05], see also Proposition 4.36). In particular, discrete logarithmic singularity types are of mod”