On the existence of Evans potentials

Hansen W, Netuka I (2013)
Mathematische Annalen 356(4): 1283-1302.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Hansen, WolfhardUniBi; Netuka, Ivan
Abstract / Bemerkung
It is shown that, for every noncompact parabolic Riemannian manifold and every nonpolar compact in , there exists a positive harmonic function on which tends to at infinity. (This is trivial for , easy for , and known for parabolic Riemann surfaces.) In fact, the statement is proven, more generally, for any noncompact connected Brelot harmonic space , where constants are the only positive superharmonic functions and, for every nonpolar compact set , there is a symmetric (positive) Green function for . 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 (the union of the parallel half-lines , and the line segments ).
Erscheinungsjahr
2013
Zeitschriftentitel
Mathematische Annalen
Band
356
Ausgabe
4
Seite(n)
1283-1302
ISSN
0025-5831
Page URI
https://pub.uni-bielefeld.de/record/2622234

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Hansen W, Netuka I. On the existence of Evans potentials. Mathematische Annalen. 2013;356(4):1283-1302.
Hansen, W., & Netuka, I. (2013). On the existence of Evans potentials. Mathematische Annalen, 356(4), 1283-1302. doi:10.1007/s00208-012-0873-2
Hansen, W., and Netuka, I. (2013). On the existence of Evans potentials. Mathematische Annalen 356, 1283-1302.
Hansen, W., & Netuka, I., 2013. On the existence of Evans potentials. Mathematische Annalen, 356(4), p 1283-1302.
W. Hansen and I. Netuka, “On the existence of Evans potentials”, Mathematische Annalen, vol. 356, 2013, pp. 1283-1302.
Hansen, W., Netuka, I.: On the existence of Evans potentials. Mathematische Annalen. 356, 1283-1302 (2013).
Hansen, Wolfhard, and Netuka, Ivan. “On the existence of Evans potentials”. Mathematische Annalen 356.4 (2013): 1283-1302.