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  • 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. (en)
Title
  • On the existence of Evans potentials
  • On the existence of Evans potentials (en)
skos:prefLabel
  • On the existence of Evans potentials
  • On the existence of Evans potentials (en)
skos:notation
  • RIV/00216208:11320/13:10174033!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita
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  • P(GA201/07/0388), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 4
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  • 93876
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  • RIV/00216208:11320/13:10174033
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  • parabolic Riemannian manifold; Evans potential; Brelot harmonic space (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [D30A2F6E5425]
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  • Mathematische Annalen
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http://linked.open...v/svazekPeriodika
  • 356
http://linked.open...iv/tvurceVysledku
  • Netuka, Ivan
  • Hansen, Wolfhard
http://linked.open...ain/vavai/riv/wos
  • 000321391300003
http://linked.open...n/vavai/riv/zamer
issn
  • 0025-5831
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s00208-012-0873-2
http://localhost/t...ganizacniJednotka
  • 11320
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