Plurisubharmonic functions and real submanifolds of $\C^n$

Bo Berndtsson

Plurisubharmonic functions and real submanifolds of $\C^n$

Complex Variables 2022-10-25 v2

Authors: Bo Berndtsson

Abstract

We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold $M$ . Applications are given to the Hausdorff measure of the intersection of the variety with $M$ and the exponential integrability of plurisubharmonic functions on $M$ .

Keywords

plurisubharmonic functions real submanifolds analytic varieties positive closed currents hausdorff measure exponential integrability

Cite

@article{arxiv.2210.00530,
  title  = {Plurisubharmonic functions and real submanifolds of $\C^n$},
  author = {Bo Berndtsson},
  journal= {arXiv preprint arXiv:2210.00530},
  year   = {2022}
}

Comments

9 pages. In the revision credit is given to an earlier paper by Duc Viet Vu where a similar result as our Theorem 1.1 appears

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