Vero - Wikipedia:WikiProject Mathematics/PlanetMath Exchange/32-XX Several complex variables and analytic spaces

32-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: complex Hessian matrix, id=6062 -- WP guess: complex Hessian matrix -- Status:

• PM: complex line, id=6018 -- WP guess: complex line -- Status:

• PM: polydisc, id=6030 -- WP: polydisc -- Status: C

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

• 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=9313^new! -- WP guess: derivative of exponential function -- Status:

• PM: exponential function defined as limit of powers, id=9312^new! -- WP guess: exponential function defined as limit of powers -- Status:

• PM: monotonicity of the sequence (1 + x/n)^n, id=9315^new! -- WP guess: monotonicity of the sequence (1 + x/n)^n -- Status:

• PM: proof of growth of exponential function, id=7774^new! -- WP guess: proof of growth of exponential function -- Status:

32A07 Special domains (Reinhardt, Hartogs, circular, tube)

• PM: analytic polyhedron, id=6091 -- WP guess: analytic polyhedron -- Status: M

  -- Taku (talk) 02:05, 23 February 2009 (UTC)

• PM: logarithmically convex set, id=6027 -- WP guess: logarithmically convex set -- Status:

• PM: Reinhardt domain, id=6029 -- WP guess: Reinhardt domain -- Status: C

  -- Taku (talk) 02:05, 23 February 2009 (UTC)

• 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

• PM: domain of holomorphy, id=6026 -- WP: domain of holomorphy -- Status: C

Oleg Alexandrov (talk) 01:51, 25 November 2005 (UTC)

• PM: Hartogs's theorem on separate analyticity, id=6024 -- WP: Hartogs's theorem on separate analyticity -- Status: M

Oleg Alexandrov (talk) 01:51, 25 November 2005 (UTC)

• PM: holomorphic functions of several variables, id=7465 -- WP guess: holomorphic functions of several variables -- Status:

32A17 Special families of functions

• PM: Weierstrass polynomial, id=6795 -- WP guess: Weierstrass polynomial -- Status:

32A20 Meromorphic functions

• PM: meromorphic functions of several variables, id=8058^new! -- WP guess: meromorphic functions of several variables -- Status:

32A22 Nevanlinna theory (local); growth estimates; other inequalities

• PM: Nevanlinna theory, id=7529 -- WP guess: Nevanlinna theory -- Status:

32A25 Integral representations; canonical kernels (Szeg�, Bergman, etc.)

• PM: Bergman kernel, id=6802 -- WP guess: Bergman kernel -- Status:

32A36 Bergman spaces

• PM: Bergman space, id=6801 -- WP guess: Bergman space -- Status:

32A60 Zero sets of holomorphic functions

• 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:

32B05 Analytic algebras and generalizations, preparation theorems

• PM: Weierstrass preparation theorem, id=6796 -- WP guess: Weierstrass preparation theorem -- Status:

32B10 Germs of analytic sets, local parametrization

• PM: Puiseux parametrization, id=7162 -- WP guess: Puiseux parametrization -- Status:

• PM: Puiseux series, id=7161 -- WP guess: Puiseux series -- Status:

32C15 Complex spaces

• 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)

32E05 Holomorphically convex complex spaces, reduction theory

• PM: holomorphically convex, id=6798 -- WP guess: holomorphically convex -- Status:

32E10 Stein spaces, Stein manifolds

• PM: Stein manifold, id=6799 -- WP guess: Stein manifold -- Status:

32E40 The Levi problem

• PM: solution of the Levi problem, id=6060 -- WP guess: solution of the Levi problem -- Status:

32F45 Invariant metrics and pseudodistances

• PM: Bergman metric, id=6803 -- WP guess: Bergman metric -- Status:

32F99 Miscellaneous

• PM: star-shaped region, id=4182 -- WP guess: star-shaped region -- Status:

32H02 Holomorphic mappings, (holomorphic) embeddings and related questions

• PM: biholomorphically equivalent, id=6032 -- WP: biholomorphically equivalent -- Status: C

Oleg Alexandrov (talk) 02:06, 24 July 2006 (UTC)

• PM: Bloch's theorem, id=3733 -- WP guess: Bloch's theorem -- Status:

• PM: Hartogs' theorem, id=3892 -- WP guess: Hartogs' lemma -- Status: A

Oleg Alexandrov (talk) 02:37, 25 November 2005 (UTC)

• PM: Hartogs extension theorem, id=7491 -- WP guess: Hartogs extension theorem -- Status: A

Taku (talk) 02:31, 23 February 2009 (UTC)

• PM: Bloch's constant, id=7983^new! -- WP guess: Bloch's constant -- Status:

• PM: Landau's constant, id=7984^new! -- WP guess: Landau's constant -- Status:

32H25 Picard-type theorems and generalizations

• PM: little Picard theorem, id=3734 -- WP guess: little Picard theorem -- Status:

• PM: Picard's theorem, id=3735 -- WP guess: Picard's theorem -- Status:

32Q60 Almost complex manifolds

• PM: Newlander-Niremberg theorem, id=7559 -- WP guess: Newlander-Niremberg theorem -- Status:

32Q99 Miscellaneous

• PM: complex analytic manifold, id=6800 -- WP guess: complex analytic manifold -- Status:

32T05 Domains of holomorphy

• PM: analytic disc, id=6052 -- WP guess: analytic disc -- Status:

• PM: Behnke-Stein theorem, id=6061 -- WP guess: Behnke-Stein theorem -- Status: C

Taku (talk) 02:41, 23 February 2009 (UTC)

• 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

Oleg Alexandrov (talk) 01:39, 25 November 2005 (UTC)

• PM: Kontinuitätssatz, id=7787^new! -- WP guess: Kontinuitätssatz -- Status:

32T15 Strongly pseudoconvex domains

• PM: biholomorphisms of strongly pseudoconvex domains extend to the boundary, id=8965^new! -- WP guess: biholomorphisms of strongly pseudoconvex domains extend to the boundary -- Status:

32T35 Exhaustion functions

• PM: exhaustion function, id=6092 -- WP guess: exhaustion function -- Status:

• PM: method of exhaustion, id=4667 -- WP guess: method of exhaustion -- Status:

32U05 Plurisubharmonic functions and generalizations

• PM: Hartogs functions, id=6025 -- WP guess: Hartogs functions -- Status:

32V05 CR structures, CR operators, and generalizations

• 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

• PM: CR function, id=6647 -- WP guess: CR function -- Status:

32V40 Real submanifolds in complex manifolds

• PM: submanifold, id=6440 -- WP guess: submanifold -- Status:

32V99 Miscellaneous

• PM: Lewy hypersurface, id=6478 -- WP guess: Lewy hypersurface -- Status: