Wikipedia:WikiProject Mathematics/PlanetMath Exchange/32-XX Several complex variables and analytic spaces
This page provides a list of all articles available at PlanetMath in the following topic:
- 32-XX Several complex variables and analytic spaces.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
32-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
edit- PM: complex Hessian matrix, id=6062 -- WP guess: complex Hessian matrix -- Status:
- PM: complex line, id=6018 -- WP guess: complex line -- Status:
- Oleg Alexandrov 23:53, 12 Mar 2005 (UTC)
- PM: several complex variables, id=6951 -- WP guess: several complex variables -- Status:
32A05 Power series, series of functions
edit- PM: exponential function, id=2541 -- WP guess: exponential function -- Status:
- PM: growth of exponential function, id=6532 -- WP guess: growth of exponential function -- Status:
- PM: derivative of exponential function, id=9313new! -- WP guess: derivative of exponential function -- Status:
- PM: exponential function defined as limit of powers, id=9312new! -- WP guess: exponential function defined as limit of powers -- Status:
- PM: monotonicity of the sequence (1 + x/n)^n, id=9315new! -- WP guess: monotonicity of the sequence (1 + x/n)^n -- Status:
- PM: proof of growth of exponential function, id=7774new! -- WP guess: proof of growth of exponential function -- Status:
32A07 Special domains (Reinhardt, Hartogs, circular, tube)
edit- PM: analytic polyhedron, id=6091 -- WP guess: analytic polyhedron -- Status: M
- PM: logarithmically convex set, id=6027 -- WP guess: logarithmically convex set -- Status:
- PM: Reinhardt domain, id=6029 -- WP guess: Reinhardt domain -- Status: C
- PM: tube domain, id=6093 -- WP guess: tube domain -- Status:
- PM: Cauchy integral formula in several variables, id=7466 -- WP guess: Cauchy integral formula in several variables -- Status:
32A10 Holomorphic functions
edit- PM: domain of holomorphy, id=6026 -- WP: domain of holomorphy -- Status: C
- PM: Hartogs's theorem on separate analyticity, id=6024 -- WP: Hartogs's theorem on separate analyticity -- Status: M
- PM: holomorphic functions of several variables, id=7465 -- WP guess: holomorphic functions of several variables -- Status:
32A17 Special families of functions
edit- PM: Weierstrass polynomial, id=6795 -- WP guess: Weierstrass polynomial -- Status:
32A20 Meromorphic functions
edit- PM: meromorphic functions of several variables, id=8058new! -- WP guess: meromorphic functions of several variables -- Status:
32A22 Nevanlinna theory (local); growth estimates; other inequalities
edit- PM: Nevanlinna theory, id=7529 -- WP guess: Nevanlinna theory -- Status:
32A25 Integral representations; canonical kernels (Szeg�, Bergman, etc.)
edit- PM: Bergman kernel, id=6802 -- WP guess: Bergman kernel -- Status:
32A36 Bergman spaces
edit- PM: Bergman space, id=6801 -- WP guess: Bergman space -- Status:
32A50 Harmonic analysis of several complex variables
edit32A60 Zero sets of holomorphic functions
edit- PM: analytic set, id=6696 -- WP guess: analytic set -- Status:
- PM: intersection of complex analytic varieties is a complex analytic variety, id=6697 -- WP guess: intersection of complex analytic varieties is a complex analytic variety -- Status:
- PM: irreducible component, id=6806 -- WP guess: irreducible component -- Status:
- PM: Remmert-Stein theorem, id=6805 -- WP guess: Remmert-Stein theorem -- Status:
32A99 Miscellaneous
edit32Axx Holomorphic functions of several complex variables
edit32B05 Analytic algebras and generalizations, preparation theorems
edit- PM: Weierstrass preparation theorem, id=6796 -- WP guess: Weierstrass preparation theorem -- Status:
32B10 Germs of analytic sets, local parametrization
edit- PM: Puiseux parametrization, id=7162 -- WP guess: Puiseux parametrization -- Status:
- PM: Puiseux series, id=7161 -- WP guess: Puiseux series -- Status:
32B20 Semi-analytic sets and subanalytic sets
edit32Bxx Local analytic geometry
edit32C15 Complex spaces
edit- PM: Riemann sphere, id=4469 -- WP: Riemann sphere -- Status: A
- There are a few things that could be copied over, but would require some careful thinking. Overall, the WP article is better. Oleg Alexandrov 05:28, 16 Feb 2005 (UTC)
32C25 Analytic subsets and submanifolds
edit32Cxx Analytic spaces
edit32E05 Holomorphically convex complex spaces, reduction theory
edit- PM: holomorphically convex, id=6798 -- WP guess: holomorphically convex -- Status:
32E10 Stein spaces, Stein manifolds
edit- PM: Stein manifold, id=6799 -- WP guess: Stein manifold -- Status:
32E40 The Levi problem
edit- PM: solution of the Levi problem, id=6060 -- WP guess: solution of the Levi problem -- Status:
32Exx Holomorphic convexity
edit32F45 Invariant metrics and pseudodistances
edit- PM: Bergman metric, id=6803 -- WP guess: Bergman metric -- Status:
32F99 Miscellaneous
edit- PM: star-shaped region, id=4182 -- WP guess: star-shaped region -- Status:
32Fxx Geometric convexity
edit32H02 Holomorphic mappings, (holomorphic) embeddings and related questions
edit- PM: biholomorphically equivalent, id=6032 -- WP: biholomorphically equivalent -- Status: C
- PM: Bloch's theorem, id=3733 -- WP guess: Bloch's theorem -- Status:
- PM: Hartogs' theorem, id=3892 -- WP guess: Hartogs' lemma -- Status: A
- PM: Hartogs extension theorem, id=7491 -- WP guess: Hartogs extension theorem -- Status: A
- PM: Bloch's constant, id=7983new! -- WP guess: Bloch's constant -- Status:
- PM: Landau's constant, id=7984new! -- WP guess: Landau's constant -- Status:
32H25 Picard-type theorems and generalizations
edit- PM: little Picard theorem, id=3734 -- WP guess: little Picard theorem -- Status:
- PM: Picard's theorem, id=3735 -- WP guess: Picard's theorem -- Status:
32Hxx Holomorphic mappings and correspondences
edit32Q60 Almost complex manifolds
edit- PM: Newlander-Niremberg theorem, id=7559 -- WP guess: Newlander-Niremberg theorem -- Status:
32Q99 Miscellaneous
edit- PM: complex analytic manifold, id=6800 -- WP guess: complex analytic manifold -- Status:
32Qxx Complex manifolds
edit32T05 Domains of holomorphy
edit- PM: analytic disc, id=6052 -- WP guess: analytic disc -- Status:
- PM: Behnke-Stein theorem, id=6061 -- WP guess: Behnke-Stein theorem -- Status: C
- PM: Hartogs triangle, id=6059 -- WP guess: Hartogs triangle -- Status:
- PM: Levi pseudoconvex, id=6048 -- WP guess: Levi pseudoconvex -- Status:
- PM: pseudoconvex, id=6056 -- WP: pseudoconvex -- Status: C
- PM: Kontinuitätssatz, id=7787new! -- WP guess: Kontinuitätssatz -- Status:
32T15 Strongly pseudoconvex domains
edit- PM: biholomorphisms of strongly pseudoconvex domains extend to the boundary, id=8965new! -- WP guess: biholomorphisms of strongly pseudoconvex domains extend to the boundary -- Status:
32T35 Exhaustion functions
edit- PM: exhaustion function, id=6092 -- WP guess: exhaustion function -- Status:
- PM: method of exhaustion, id=4667 -- WP guess: method of exhaustion -- Status:
32Txx Pseudoconvex domains
edit32U05 Plurisubharmonic functions and generalizations
edit- PM: Hartogs functions, id=6025 -- WP guess: Hartogs functions -- Status:
32U10 Plurisubharmonic exhaustion functions
edit32Uxx Pluripotential theory
edit32V05 CR structures, CR operators, and generalizations
edit- PM: CR submanifold, id=6479 -- WP guess: CR submanifold -- Status:
- PM: generic manifold, id=6623 -- WP guess: generic manifold -- Status:
- PM: totally real submanifold, id=6624 -- WP guess: totally real submanifold -- Status:
32V10 CR functions
edit- PM: CR function, id=6647 -- WP guess: CR function -- Status:
32V40 Real submanifolds in complex manifolds
edit- PM: submanifold, id=6440 -- WP guess: submanifold -- Status:
32V99 Miscellaneous
edit- PM: Lewy hypersurface, id=6478 -- WP guess: Lewy hypersurface -- Status: