scholarly journals On local hulls of Levi-flat hypersurfaces

2021 ◽  
pp. 2150050
Author(s):  
Rasul Shafikov ◽  
Alexandre Sukhov
Keyword(s):  
Singular Points ◽  
Polynomial Convexity ◽  
Local Polynomial ◽  
Real Analytic

We discuss local polynomial convexity of real analytic Levi-flat hypersurfaces in [Formula: see text], [Formula: see text], near singular points.

scholarly journals POLYNOMIAL APPROXIMATION, LOCAL POLYNOMIAL CONVEXITY, AND DEGENERATE CR SINGULARITIES — II

2011 ◽  
Vol 22 (12) ◽  
pp. 1721-1733 ◽  
Author(s):  
GAUTAM BHARALI
Keyword(s):  
Approximation Theorem ◽  
Sufficient Conditions ◽  
Hölder Continuous ◽  
Polynomial Convexity ◽  
Closed Disk ◽  
Local Polynomial ◽  
Polynomially Convex ◽  
Polynomial Hull ◽  
Weierstrass Approximation Theorem ◽  
Almost All

We provide some conditions for the graph of a Hölder-continuous function on [Formula: see text], where [Formula: see text] is a closed disk in ℂ, to be polynomially convex. Almost all sufficient conditions known to date — provided the function (say F) is smooth — arise from versions of the Weierstrass Approximation Theorem on [Formula: see text]. These conditions often fail to yield any conclusion if rank ℝDF is not maximal on a sufficiently large subset of [Formula: see text]. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in ℂ2 at an isolated complex tangency.

A Real-analytic Nonpolynomially Convex Isotropic Torus with no Attached Discs

2018 ◽  
Vol 61 (2) ◽  
pp. 289-291
Author(s):  
Purvi Gupta
Keyword(s):  
Polynomial Convexity ◽  
Analytic Case ◽  
Real Analytic ◽  
Holomorphic Discs ◽  
Isotropic Torus

AbstractWe showbymeans of an example in that Gromov’s theoremon the presence of attached holomorphic discs for compact Lagrangianmanifolds is not true in the subcritical real-analytic case, even in the absence of an obvious obstruction, i.e., polynomial convexity.

scholarly journals Local polynomial convexity of certain graphs in C 3

2009 ◽  
Vol 58 (2) ◽  
pp. 479-488 ◽  
Author(s):  
Nguyen Quang Dieu ◽  
Kieu Phuong Chi
Keyword(s):  
Polynomial Convexity ◽  
Local Polynomial

Binary diagrams of mesomorphous compounds exhibiting singular points

1978 ◽  
Vol 3 ◽  
pp. 381-386 ◽  
Author(s):  
F. Hardouin ◽  
G. Sigaud ◽  
M.-F. Achard ◽  
H. Gasparoux
Keyword(s):  
Singular Points

Effect of proximity of the Fermi level to singular points in the band structure on the kinetic and lattice properties of metals and alloys

1988 ◽  
Vol 154 (3) ◽  
pp. 525 ◽  
Author(s):  
V.P. Antropov ◽  
Valentin G. Vaks ◽  
M.I. Katsnel'son ◽  
V.G. Koreshkov ◽  
A.I. Likhtenshtein ◽  
...  
Keyword(s):  
Band Structure ◽  
Fermi Level ◽  
Metals And Alloys ◽  
Singular Points
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