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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 5, Pages 1102–1108 (Mi izv1221)  

This article is cited in 5 scientific papers (total in 5 papers)

Stochastically complete manifolds and summable harmonic functions

A. A. Grigor'yan


Abstract: Main result: if on a geodesically complete Riemannian manifold $M$ the volume $V_R$ of a geodesic ball of radius $R$ with fixed center satisfies the condition $\displaystyle\int^\infty\frac{R dR}{\ln V_R}=\infty$ then every nonnegative integrable superharmonic function on $M$ is equal to a constant.
Bibliography: 18 titles.

Full text: PDF file (981 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:2, 425–432

Bibliographic databases:

UDC: 517.95
MSC: Primary 53C20, 31B05, 60J60; Secondary 53C22, 30D20, 35J05, 34B27
Received: 29.04.1986

Citation: A. A. Grigor'yan, “Stochastically complete manifolds and summable harmonic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 52:5 (1988), 1102–1108; Math. USSR-Izv., 33:2 (1989), 425–432

Citation in format AMSBIB
\Bibitem{Gri88}
\by A.~A.~Grigor'yan
\paper Stochastically complete manifolds and summable harmonic functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 5
\pages 1102--1108
\mathnet{http://mi.mathnet.ru/izv1221}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972099}
\zmath{https://zbmath.org/?q=an:0677.60086|0661.60090}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 2
\pages 425--432
\crossref{https://doi.org/10.1070/IM1989v033n02ABEH000850}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Sitaram, G. A. Willis, “Lp-functions satisfying the mean value property on homogeneous spaces”, JAZ, 56:03 (1994), 384  crossref
    2. Ilkka Holopainen, “A sharpL q-Liouville theorem forp-harmonic functions”, Isr J Math, 115:1 (2000), 363  crossref  mathscinet  zmath  isi
    3. V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “On uniqueness problems related to elliptic equations for measures”, J Math Sci, 2011  crossref
    4. V. I. Bogachev, A. I. Kirillov, S. V. Shaposhnikov, “Integrable solutions of the stationary Kolmogorov equation”, Dokl. Math, 85:3 (2012), 309  crossref
    5. I. A. Alexandrova, J. Mikeš, S. E. Stepanov, I. I. Tsyganok, “Theorems of Liuville types in theory mappings of the complete Riemannian manifolds”, J. Math. Sci., 221:6 (2017), 737–744  mathnet  crossref  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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