scholarly journals A symmetry property for polyharmonic functions vanishing on equidistant hyperplanes

2016 ◽  
Vol 290 (7) ◽  
pp. 1087-1096 ◽  
Author(s):  
Ognyan Kounchev ◽  
Hermann Render
Keyword(s):  
Symmetry Property ◽  
Polyharmonic Functions

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

scholarly journals Bounded polyharmonic functions and the dimension of the manifold

1973 ◽  
Vol 13 (3) ◽  
pp. 529-535 ◽  
Author(s):  
Norman Mirsky ◽  
Leo Sario ◽  
Cecilia Wang
Keyword(s):  
Polyharmonic Functions

scholarly journals Riesz-Martin representation for positive super-polyharmonic functions in A Riemannian manifold

2006 ◽  
Vol 2006 ◽  
pp. 1-9
Author(s):  
V. Anandam ◽  
S. I. Othman
Keyword(s):  
Riemannian Manifold ◽  
Complex Plane ◽  
Unit Disc ◽  
Biharmonic Function ◽  
Subharmonic Functions ◽  
Polyharmonic Functions ◽  
Superharmonic Functions ◽  
Martin Representation

Letube a super-biharmonic function, that is,Δ2u≥0, on the unit discDin the complex plane, satisfying certain conditions. Then it has been shown thatuhas a representation analogous to the Poisson-Jensen representation for subharmonic functions onD. In the same vein, it is shown here that a functionuon any Green domainΩin a Riemannian manifold satisfying the conditions(−Δ)iu≥0for0≤i≤mhas a representation analogous to the Riesz-Martin representation for positive superharmonic functions onΩ.

Adsorption‐stretching analogy for a polymer chain on a plane. Symmetry property of the phase diagram

1994 ◽  
Vol 100 (3) ◽  
pp. 2325-2334 ◽  
Author(s):  
Aleksandr M. Skvortsov ◽  
Aleksey A. Gorbunov ◽  
Leonid I. Klushin
Keyword(s):  
Phase Diagram ◽  
Polymer Chain ◽  
Symmetry Property ◽  
Plane Symmetry
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