What does pseudoconvexity mean?
Definitions for pseudoconvexity
pseu·do·con·vex·i·ty
This dictionary definitions page includes all the possible meanings, example usage and translations of the word pseudoconvexity.
Wiktionary
pseudoconvexitynoun
The property of being pseudoconvex.
Wikidata
Pseudoconvexity
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 C. 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 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 convex set is pseudoconvex. When has a 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, If 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 boundary which are relatively compact in, such that∞
Numerology
Chaldean Numerology
The numerical value of pseudoconvexity in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of pseudoconvexity in Pythagorean Numerology is: 1
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"pseudoconvexity." Definitions.net. STANDS4 LLC, 2024. Web. 17 Apr. 2024. <https://www.definitions.net/definition/pseudoconvexity>.
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