DOI QR코드

DOI QR Code

ASYMPTOTIC DIRICHLET PROBLEM FOR THE SCHRÖDINGER OPERATOR ON 2-DIMENSIONAL CARTAN-HADAMARD MANIFOLDS

  • Kim, Seok-Woo (Department of Mathematics Education Konkuk University) ;
  • Lee, Yong-Hah (Department of Mathematics Education Ewha Womans University)
  • 발행 : 2007.10.31

초록

We solve the asymptotic Dirichlet problem for a certain $Schr\"{o}dinger$ operator on 2-dimensional Cartan-Hadamard manifolds.

키워드

참고문헌

  1. A. Ancona, Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature, Rev. Mat. Iberoamericana 10 (1994), 189-220
  2. H. I. Choi, Asymptotic Dirichlet problem for harmonic functions on Riemannian manifolds, Trans. Amer. Math. Soc. 281 (1984), 691-716 https://doi.org/10.2307/2000080
  3. P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45-109 https://doi.org/10.2140/pjm.1973.46.45
  4. A. A. Grigor'yan and W. Hansen, Liouville property for Schrodinqer operators, Math. Ann. 312 (1998), 659-716 https://doi.org/10.1007/s002080050241