Boundary behaviour of solutions to the Generalised Weinstein Equation

1989 ◽  
pp. 24-38 ◽  
Author(s):  
Ömer Akin
Keyword(s):  
Boundary Behaviour ◽  
Weinstein Equation

scholarly journals Function-Theoretic Metrics and Boundary Behaviour of Functions Meromorphic or Holomorphic in the Unit Disk

1972 ◽  
Vol 45 ◽  
pp. 109-117
Author(s):  
Shinji Yamashita
Keyword(s):  
Unit Disk ◽  
Boundary Behaviour ◽  
Arc Length

The metrics to which the title of the present paper refers are expressed in the form of elements of arc length as follows:

Boundary behaviour for solutions of elliptic singular equations with a gradient term

2008 ◽  
Vol 69 (12) ◽  
pp. 4550-4566 ◽  
Author(s):  
F. Cuccu ◽  
E. Giarrusso ◽  
G. Porru
Keyword(s):  
Gradient Term ◽  
Boundary Behaviour ◽  
Singular Equations

scholarly journals Boundary behaviour of special cohomology classes arising from the Weil representation

2012 ◽  
Vol 12 (3) ◽  
pp. 571-634 ◽  
Author(s):  
Jens Funke ◽  
John Millson
Keyword(s):  
Modular Forms ◽  
Symmetric Spaces ◽  
Theta Functions ◽  
Theta Series ◽  
Siegel Modular Forms ◽  
Boundary Behaviour ◽  
Orthogonal Groups ◽  
Local Coefficients ◽  
Generating Series ◽  
Vector Valued

AbstractIn our previous paper [J. Funke and J. Millson, Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms, American J. Math. 128 (2006), 899–948], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces $X$ attached to real orthogonal groups of type $(p, q)$. This correspondence is realized using theta functions associated with explicitly constructed ‘special’ Schwartz forms. Furthermore, the theta functions give rise to generating series of certain ‘special cycles’ in $X$ with coefficients.In this paper, we study the boundary behaviour of these theta functions in the non-compact case and show that the theta functions extend to the Borel–Sere compactification $ \overline{X} $ of $X$. However, for the $ \mathbb{Q} $-split case for signature $(p, p)$, we have to construct and consider a slightly larger compactification, the ‘big’ Borel–Serre compactification. The restriction to each face of $ \overline{X} $ is again a theta series as in [J. Funke and J. Millson, loc. cit.], now for a smaller orthogonal group and a larger coefficient system.As an application we establish in certain cases the cohomological non-vanishing of the special (co)cycles when passing to an appropriate finite cover of $X$. In particular, the (co)homology groups in question do not vanish. We deduce as a consequence a sharp non-vanishing theorem for ${L}^{2} $-cohomology.

scholarly journals On boundary behaviour of symplectomorphisms

1998 ◽  
Vol 21 (3) ◽  
pp. 285-305
Author(s):  
Elisabetta Barletta ◽  
Sorin Dragomir
Keyword(s):  
Boundary Behaviour
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