scholarly journals On polynomial convexity of compact subsets of totally-real submanifolds in Cn

2017 ◽  
Vol 448 (2) ◽  
pp. 1305-1317
Author(s):  
Sushil Gorai
Keyword(s):  
Real Submanifolds ◽  
Polynomial Convexity ◽  
Totally Real ◽  
Compact Subsets

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).

Polynomial convexity and totally real manifolds

2009 ◽  
Vol 54 (3-4) ◽  
pp. 265-281 ◽  
Author(s):  
Erik Løw ◽  
Erlend Fornæss Wold
Keyword(s):  
Polynomial Convexity ◽  
Totally Real

scholarly journals Characterizing a class of totally real submanifolds of $S^6$ by their sectional curvatures

1995 ◽  
Vol 47 (2) ◽  
pp. 185-198 ◽  
Author(s):  
Bang-Yen Chen ◽  
Franki Dillen ◽  
Leopold Verstraelen ◽  
Luc Vrancken
Keyword(s):  
Real Submanifolds ◽  
Sectional Curvatures ◽  
Totally Real
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