본문 바로가기
KERD
논문KCI 등재

Polynomial growth harmonic maps on complete Riemannian manifolds

Polynomial growth harmonic maps on complete Riemannianmanifolds

이영하
대한수학회 (The Korean Mathematical Society)|2004.08|대한수학회보 (Bulletin of the KMS)|제41권 제3호|pp. 521-540

1

조회

0

다운로드

0

인용

0

참고문헌

주제분류수학

초록

Abstract

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hullcontaining the image of harmonic mapswith polynomial growth rate on a certain class of manifoldsinto a Cartan-Hadamard manifold with sectional curvature boundedby two negative constants.We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifoldinto a regular ball in terms of massive subsets,in the case when the space of bounded harmonic functions on the manifold is finite dimensional.

참고문헌 (28)

  1. "The Liouville theorem for harmonic maps", 36, pp.147~ (1980)
  2. "Harmonic maps with finite total energy,Proc. Amer. Math. Soc. 124 (1996) 275--284.", 124, pp.275~284 (1996)
  3. "On function theory on spaceswith a lower Ricci curvature bound", 3, pp.241~246 (1996)
  4. "^Harmonic functions with polynomial growth", 46, pp.1~77 (1997)
  5. "Large scale behavior of kernels of Schr"odingeroperators", 117, pp.1355~1398 (1997)
  6. "^Generalized Liouville properties for manifolds", 3, pp.723~729 (1996)
  7. "^Harmonic functions on manifolds", 146, pp.725~747 (1997)
  8. "Liouville theorems for harmonic sections andapplications", 51(2), pp.113~138 (1998)
  9. "Weyl type bounds for harmonic functions", 131, pp.257~298 (1998)
  10. Coulhon, "Vari'et'es riemanniennes isom'etriques 'a l'infini", 11, pp.687~726 (1995)
  11. "A priori estimates for harmonic mappings", 336, pp.124~ (1982)
  12. "Convex functions and harmonic maps", 33, pp.433~ (1972)
  13. "Dimension of space of harmonic functions English transl. in Math. Notes", pp.55 1114~
  14. "The heat equation on noncompact Riemannianmanifolds Englishtransl. in Math. USSR-Sb.", (1), pp.55 47~
  15. "Uniqueness and stability of harmonicmaps and their Jacobi fields", pp.269~ (1979)
  16. "and combinatorial approximations of geometriesof non-compact riemannian manifolds", (3), pp.391~ (1985)
  17. "and harmonic maps with small image I", pp.371~ (1990)
  18. "Generalized Liouville property for Schr"odinger operatoron Riemannian manifolds", 238, pp.355~387 (2001)
  19. "Asymptotic Dirichlet problem for harmonic maps via rough isometry", 12, pp.37~49 (2000)
  20. "Polynomial growth harmonic functions on complete Riemannian manifolds"
  21. "Polynomial growth harmonic sections", 4, pp.35~44 (1997)
  22. "Green's functions, harmonic functions, and volume comparison", 41, pp.277~318 (1995)
  23. "Convex hull properties of harmonic maps", 48, pp.497~530 (1998)
  24. "Ball covering property and nonnegative Ricci curvature outside a compact set", 54, pp.459~ (1993)
  25. "Classification theory of Riemann surfaces" (1970), Springer-Verlag
  26. "Bounded harmonic maps on a class of manifolds", 124, pp.2241~2248. (1996)
  27. "A note on harmonic forms on complete manifolds", 128, pp.3097~3108 (1998)
  28. "Harmonic functions on complete Riemannian manifolds", 28, pp.201~ (1975)

관련 논문AI추천

Asymptotic behavior of harmonic maps and exponentially harmonic functions장정욱, 지동표, Gundon Choi대한수학회 · 대한수학회지2002 · 제39권 제5호ASYMPTOTIC DIRICHLET PROBLEM FOR HARMONIC MAPS ON NEGATIVELY CURVED MANIFOLDS김석우, 이용하대한수학회 · 대한수학회지2005 · 제42권 제3호A Liouville type theorem for harmonic morphisms문동주, 정승달, Huili Liu대한수학회 · 대한수학회지2007 · 제44권 제4호Local gradient estimate on Riemannian manifold with asymptotically non-negative Ricci curvatureHui Liu, Jingjing Zhang, Lingen Lu, Tian Chong대한수학회 · 대한수학회지2025 · 제62권 제1호Liouville type theorem for p-harmonic maps II정승달대한수학회 · 대한수학회논문집2014 · 제29권 제1호Semi-conformal $L$-harmonic maps and Liouville type theoremAhmed Mohammed Cherif, Embarka Remli강원경기수학회 · 한국수학논문집2022 · 제30권 제1호

이 간행물의 다른 논문 (16건)

Postnikov sections and groups이기영pp. 393-401The uniform consistency of the sample kernel quantile process김성연, 배종식pp. 403-412Invertible and isometric composition operators on vector-valued hardy spacesUdhey Bhanu, S. D. Sharmapp. 414-418Relative projectivity and related resultsH. Ansari-Toroghypp. 419-426On the pressure of continuous transformationsKi Duk Han, 박종서, 이경복pp. 427-434
원문 보기