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Asymptotic Dirichlet problem for the Schrödinger operator via rough isometry
Author(s):
Yong
Hah
Lee
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3411-3420.
MSC (2000):
Primary 58J05;
Secondary 35J10
Posted:
June 20, 2005
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Additional information
Abstract:
We pose and solve the asymptotic Dirichlet problem for the Schrödinger operator via rough isometries on a certain class of Riemannian manifolds. With suitable potentials, we give the solvability of the problem for a naturally defined class of data functions.
References:
-
- 1.
- M. T. Anderson, The Dirichlet problem at infinity for manifolds of negative curvature, J. Differential Geom. 18 (1983), 701-721. MR 0730923 (85m:58178)
- 2.
- M. T. Anderson and R. Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math. 121 (1985), 429-461. MR 0794369 (87a:58151)
- 3.
- P. Buser, A note on the isoperimetric constant, Ann. Sci. Ec. Norm. Sup. Paris 15 (1982), 213-230. MR 0683635 (84e:58076)
- 4.
- S. Y. Cheng, The Dirichlet problem at infinity for nonpositively curved manifolds, Comm. Anal. Geom. 1 (1993), 101-112. MR 1230275 (94h:53048)
- 5.
- H. I. Choi, Asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds, Trans. Amer. Math. Soc. 281 (1984), 691-716. MR 0722769 (85b:53040)
- 6.
- H. I. Choi, S. W. Kim and Y. H. Lee, Rough isometry and the asymptotic Dirichlet problem, Tôhoku Math. J. 50 (1998), 333-348. MR 1638223 (99j:58211)
- 7.
- Th. Coulhon and L. Saloff-Coste, Variétés riemanniennes isométriques à l'infini, Rev. Mat. Iberoamericana 11 (1995), 687-726. MR 1363211 (96m:53035)
- 8.
- A. A. Grigor'yan and W. Hansen, Liouville property for Schrödinger operators, Math. Ann. 312 (1998), 659-716. MR 1660247 (2000a:58092)
- 9.
- P. Li and J. Wang, On harmonic rough isometries into Hadamard space, Asian J. Math. 2 (1998), 419-442. MR 1724623 (2000j:53055)
- 10.
- M. Kanai, Rough isometries, and combinatorial approximations of geometries of non-compact Riemannian manifolds, J. Math. Soc. Japan 37 No.3 (1985), 391-413. MR 0792983 (87d:53082)
- 11.
- R. Schoen and S. T. Yau, Lectures on Differential Geometry, International Press, Boston, 1994. MR 1333601 (97d:53001)
- 12.
- D. Sullivan, The Dirichlet problem at infinity for a negatively curved manifold, J. Differential Geom. 18 (1983), 723-732. MR 0730924 (85m:58177)
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Additional Information:
Yong
Hah
Lee
Affiliation:
Department of Mathematics Education, Ewha Womans University, Seoul 120-750, Korea
Email:
yonghah@ewha.ac.kr
DOI:
10.1090/S0002-9939-05-08265-1
PII:
S 0002-9939(05)08265-1
Keywords:
Asymptotic Dirichlet problem,
Schr\"odinger operator,
rough isometry
Received by editor(s):
September 25, 2001
Posted:
June 20, 2005
Additional Notes:
This work was supported by Korea Research Foundation Grant (KRF-2002-070-C00010)
Communicated by:
Bennett Chow
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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