Addendum to “Stationary discs and finite jet determination for non-degenerate generic real submanifolds” [Adv. Math. 343 (2019) 910–934]

2021 ◽  
Vol 383 ◽  
pp. 107701
Author(s):  
Florian Bertrand ◽  
Léa Blanc-Centi ◽  
Francine Meylan
Keyword(s):  
Real Submanifolds ◽  
Finite Jet Determination

scholarly journals Stationary discs and finite jet determination for non-degenerate generic real submanifolds

2019 ◽  
Vol 343 ◽  
pp. 910-934 ◽  
Author(s):  
Florian Bertrand ◽  
Léa Blanc-Centi ◽  
Francine Meylan
Keyword(s):  
Real Submanifolds ◽  
Finite Jet Determination

Smooth Boundary Values Along Totally Real Submanifolds

1984 ◽  
Vol 36 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Regularity Result ◽  
Boundary Values ◽  
Real Submanifolds ◽  
Strongly Pseudoconvex Domain ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Class C ◽  
Totally Real

The main result of this paper is the following regularity result:THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).

Sign in / Sign up

Export Citation Format

Share Document