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- Pseudoconvexity abstract "In mathematics, more precisely in the theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn. Pseudoconvex sets are important, as they allow for classification of domains of holomorphy. Let be a domain, that is, an open connected subset. One says that is pseudoconvex (or Hartogs pseudoconvex) if there exists a continuous plurisubharmonic function on such that the set is a relatively compact subset of for all real numbers In other words, a domain is pseudoconvex if has a continuous plurisubharmonic exhaustion function. Every (geometrically) convex set is pseudoconvex.When has a (twice continuously differentiable) boundary, this notion is the same as Levi pseudoconvexity, which is easier to work with. More specifically, with a boundary, it can be shown that has a defining function; i.e., that there exists which is so that , and . Now, is pseudoconvex iff for every and in the complex tangent space at p that is, we haveIf does not have a boundary, the following approximation result can come in useful. Proposition 1 If is pseudoconvex, then there exist bounded, strongly Levi pseudoconvex domains with (smooth) boundary which are relatively compact in , such that This is because once we have a as in the definition we can actually find a C∞ exhaustion function.".
- Pseudoconvexity wikiPageExternalLink noti798.
- Pseudoconvexity wikiPageExternalLink rtx120200301p.pdf.
- Pseudoconvexity wikiPageID "3235998".
- Pseudoconvexity wikiPageRevisionID "544209810".
- Pseudoconvexity hasPhotoCollection Pseudoconvexity.
- Pseudoconvexity id "6056".
- Pseudoconvexity title "Pseudoconvex".
- Pseudoconvexity subject Category:Several_complex_variables.
- Pseudoconvexity type PhysicalEntity100001930.
- Pseudoconvexity type SeveralComplexVariables.
- Pseudoconvexity type Thing100002452.
- Pseudoconvexity type Variable109468959.
- Pseudoconvexity comment "In mathematics, more precisely in the theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn. Pseudoconvex sets are important, as they allow for classification of domains of holomorphy. Let be a domain, that is, an open connected subset.".
- Pseudoconvexity label "Pseudoconvexity".
- Pseudoconvexity sameAs m.0909k_.
- Pseudoconvexity sameAs Q7254693.
- Pseudoconvexity sameAs Q7254693.
- Pseudoconvexity sameAs Pseudoconvexity.
- Pseudoconvexity wasDerivedFrom Pseudoconvexity?oldid=544209810.
- Pseudoconvexity isPrimaryTopicOf Pseudoconvexity.