Lemma 5.40.2`AA358481B7F6`

Lemma 5.40.2.AA358481B7F6 Let $\eta $ be a smooth semipositive real $(1,1)$-form on $X$. If an obstacle $f$ is finite almost everywhere and bounded below quasi-everywhere by a constant, then $P_\eta (f)$ is a bounded $\eta $-plurisubharmonic function.

Proof. Since $\eta \geq 0$, constants are $\eta $-plurisubharmonic, so the constant lower bound of $f$ is a competitor. The finite-sublevel argument above gives a common upper bound for all competitors. Hence $P_\eta (f)$ is an $\eta $-plurisubharmonic function lying between these two constants. $\square$

Cite this page

BibTeX citation

@misc{pome-tag-AA358481B7F6,
  author = {{Pome contributors}},
  title = {Lemma 5.40.2},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/AA358481B7F6/}
}

Comments

Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.

Read this page’s discussion on GitHub Post a comment on GitHub

Lemma 5.40.2AA358481B7F6

Comments

Lemma 5.40.2`AA358481B7F6`