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A new characterization of the analytic surfaces in 3 that satisfy the local Phragmén-Lindelöf condition

Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that an analytic surface V in a neighborhood of the origin in 3 satisfies the local Phragmén-Lindelöf condition PL loc at the origin if and only if V satisfies the following two conditions: (1) V is nearly hyperbolic; (2) for each real simple curve γ in 3 and each d 1 , the (algebraic) limit variety T γ , d V satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure k -dimensional analytic variety V to satisify PL loc .

Analyticité des conditions de Whitney strictes

Jean-Paul Speder (1973)

Annales de l'institut Fourier

Soient X un espace analytique complexe réduit de dimension pure et Y un sous-espace lisse de X de dimension pure tel que dimension Y < dimension X .L’ensemble des points de Y en lesquels les conditions de Whitney strictes ne sont pas satisfaites par ( X , Y ) est un sous-espace analytique propre de Y .

Approximation of sets defined by polynomials with holomorphic coefficients

Marcin Bilski (2012)

Annales Polonici Mathematici

Let X be an analytic set defined by polynomials whose coefficients a , . . . , a s are holomorphic functions. We formulate conditions on sequences a 1 , ν , . . . , a s , ν of holomorphic functions converging locally uniformly to a , . . . , a s , respectively, such that the sequence X ν of sets obtained by replacing a j ’s by a j , ν ’s in the polynomials converges to X.


Andrew John Sommese, James B. Carrell (1978)

Mathematica Scandinavica

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