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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10174033%21RIV14-GA0-11320___
rdf:type
skos:Concept n21:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1007/s00208-012-0873-2
dcterms:description
It is shown that, for every noncompact parabolic Riemannian manifold X and every nonpolar compact K in X, there exists a positive harmonic function on X \ K which tends to infinity at infinity. (This is trivial for R, easy for R^2, and known for parabolic Riemann surfaces.) In fact, the statement is proven, more generally, for any noncompact connected Brelot harmonic space X, where constants are the only positive superharmonic functions and, for every nonpolar compact set K, there is a symmetric (positive) Green function for X \ K. This includes the case of parabolic Riemannian manifolds. Without symmetry, however, the statement may fail. This is shown by an example, where the underlying space is a graph. It is shown that, for every noncompact parabolic Riemannian manifold X and every nonpolar compact K in X, there exists a positive harmonic function on X \ K which tends to infinity at infinity. (This is trivial for R, easy for R^2, and known for parabolic Riemann surfaces.) In fact, the statement is proven, more generally, for any noncompact connected Brelot harmonic space X, where constants are the only positive superharmonic functions and, for every nonpolar compact set K, there is a symmetric (positive) Green function for X \ K. This includes the case of parabolic Riemannian manifolds. Without symmetry, however, the statement may fail. This is shown by an example, where the underlying space is a graph.
dcterms:title
On the existence of Evans potentials On the existence of Evans potentials
skos:prefLabel
On the existence of Evans potentials On the existence of Evans potentials
skos:notation
RIV/00216208:11320/13:10174033!RIV14-GA0-11320___
n21:predkladatel
n22:orjk%3A11320
n3:aktivita
n12:Z n12:P
n3:aktivity
P(GA201/07/0388), Z(MSM0021620839)
n3:cisloPeriodika
4
n3:dodaniDat
n17:2014
n3:domaciTvurceVysledku
n14:7936699
n3:druhVysledku
n5:J
n3:duvernostUdaju
n7:S
n3:entitaPredkladatele
n10:predkladatel
n3:idSjednocenehoVysledku
93876
n3:idVysledku
RIV/00216208:11320/13:10174033
n3:jazykVysledku
n20:eng
n3:klicovaSlova
parabolic Riemannian manifold; Evans potential; Brelot harmonic space
n3:klicoveSlovo
n9:Evans%20potential n9:Brelot%20harmonic%20space n9:parabolic%20Riemannian%20manifold
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[D30A2F6E5425]
n3:nazevZdroje
Mathematische Annalen
n3:obor
n6:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n16:GA201%2F07%2F0388
n3:rokUplatneniVysledku
n17:2013
n3:svazekPeriodika
356
n3:tvurceVysledku
Hansen, Wolfhard Netuka, Ivan
n3:wos
000321391300003
n3:zamer
n19:MSM0021620839
s:issn
0025-5831
s:numberOfPages
20
n8:doi
10.1007/s00208-012-0873-2
n15:organizacniJednotka
11320