Bulletin of the American Mathematical Society

Minimality in families of solutions of $\Delta u = Pu$ on Riemannian manifolds

Kwang-nan Chow

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 77, Number 6 (1971), 1079-1081.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183533198

Mathematical Reviews number (MathSciNet)
MR0287479

Zentralblatt MATH identifier
0223.31011

Subjects
Primary: 31B10: Integral representations, integral operators, integral equations methods 31B25: Boundary behavior 31B35: Connections with differential equations
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions

Citation

Chow, Kwang-nan. Minimality in families of solutions of $\Delta u = Pu$ on Riemannian manifolds. Bull. Amer. Math. Soc. 77 (1971), no. 6, 1079--1081. https://projecteuclid.org/euclid.bams/1183533198


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References

  • 1. M. Glasner and R. Katz, A note on the Royden boundary, Bull. Amer. Math. Soc. 75 (1969), 945-947. MR 40 #394.
  • 2. M. Glasner and R. Katz, On the behavior of solutions of ∆u = Pu at the Royden boundary, J. Analyse Math. 22 (1969), 343-354. MR 41 #1995.
  • 3. M. Nakai, The space of bounded solutions of the equation ∆u = Pu on a Riemann surface, Proc. Japan Acad. 36 (1960), 267-272. MR 22 #12216.
  • 4. M. Nakai, Genus and classification of Riemann surfaces, Osaka Math. J. 14 (1962), 153-180. MR 25 #4091.
  • 5. H. L. Royden, The equation ∆u = Pu and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. AI No. 271 (1959), 27 pp. MR 22 #12215.
  • 6. L. Sario and M. Nakai, Classification theory of Riemann surfaces, Springer-Verlag, Berlin and New York, 1970.