본문 바로가기
KERD
논문KCI 등재

ASYMPTOTIC DIRICHLET PROBLEM FOR HARMONIC MAPS ON NEGATIVELY CURVED MANIFOLDS

이용하|김석우
대한수학회 (The Korean Mathematical Society)|2005.05|대한수학회지 (Journal of the KMS)|제42권 제3호|pp. 543-553

1

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

In this paper, we prove the existence of nonconstant bounded harmonic maps on a Cartan-Hadamard manifold of pinched negative curvature by solving the asymptotic Dirichlet problem. To be precise, given any continuous data f on the boundary at in¯nity with image within a ball in the normal range, we prove that there exists a unique harmonic map from the manifold into the ball with boundary value f.

참고문헌 (17)

  1. "Convexity at innity and Brownian motion on manifolds with unboundednegative curvature", pp.189~220 (1994)
  2. "The Dirichlet problem at innity of negative curvature", 18, pp.701~721 (1983)
  3. "Positive harmonic functions on complete mani-folds of negative curvature", 121, pp.429~461 (1985)
  4. S. Y. Cheng, "Liouville theorem for harmonic maps", 36, pp.147~151 (1980)
  5. null, "The Dirichlet problem at innity for nonpositively curved manifolds", 1, pp.101~112 (1993)
  6. H. I. Choi, "Asymptotic Dirichlet problem for harmonic functions on Riemannianmanifolds", 281, pp.691~ (1984)
  7. H. I. Choi,S. W. Kim, "Rough isometry and asymptotic Dirichletproblem", 50, pp.333~348 (1998)
  8. Q. Ding, "The existence of bounded harmonic functions on C-Hmanifolds", 53, pp.197~207 (1996)
  9. P. Eberlein, "Visibility manifolds", 46, pp.45~109 (1973)
  10. M. Giaquinta, "An existence theorem for harmonic mappingsof Riemannian manifolds", 336, pp.124~164 (1982)
  11. R. E. Greene, "Function theory on manifolds which possess a pole Lecture Notes in Math." (1979), Springer-Verlag
  12. E. P. Hsu, "Brownian motion and Dirichlet problems at innity", 31(3), pp.1305~1319 (2003)
  13. P. Hsu, "The limiting angle of certain Riemannian Brownian mo-tions", 38, pp.755~768 (1985)
  14. W. Jager, "Uniqueness and stability of harmonic maps and theirJacobi elds", 28, pp.269~291 (1979)
  15. R. Schoen, "Lectures on Dierential Geometry" (1994), International Press
  16. D. Sullivan, "The Dirichlet problem at innity for a negatively curved manifold", 18, pp.723~732 (1983)
  17. S. T. Yau, "Harmonic functions on complete Riemannian manifolds", 28, pp.201~228 (1975)

관련 논문AI추천

Asymptotic behavior of harmonic maps and exponentially harmonic functions장정욱, 지동표, Gundon Choi대한수학회 · 대한수학회지2002 · 제39권 제5호Polynomial growth harmonic maps on complete Riemannian manifolds이영하대한수학회 · 대한수학회보2004 · 제41권 제3호Local gradient estimate on Riemannian manifold with asymptotically non-negative Ricci curvatureHui Liu, Jingjing Zhang, Lingen Lu, Tian Chong대한수학회 · 대한수학회지2025 · 제62권 제1호Asymptotic Dirichlet problem for the Schr\＂odinger operator on 2-dimensional Cartan-Hadamard manifolds김석우, 이용하대한수학회 · 대한수학회논문집2007 · 제22권 제4호Liouville type theorem for p-harmonic maps II정승달대한수학회 · 대한수학회논문집2014 · 제29권 제1호THEOREMS OF LIOUVILLE TYPE FORQUASI-STRONGLY p-HARMONIC MAPSGabjinYun한국수학교육학회 · 이론수학과 교직수학2002 · 제9권 제2호

이 간행물의 다른 논문 (12건)

Lp ESTIMATES FOR A ROUGH MAXIMALOPERATOR ON PRODUCT SPACESHussain Mohammed Al-Qassempp. 405-434ON KENMOTSU MANIFOLDSJae Bok Jun, Uday Chand De, Goutam Pathakpp. 435-445SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP최미경, Bang-Yen Chen, Young Ho Kimpp. 447-455WEAKLY DUO RINGS WITH NIL JACOBSON RADICALNam Kyun Kim, 이양, 김홍기pp. 457-470SPACES OF CONFORMAL VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS김영호, 김동수pp. 471-484
원문 보기