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초록· 키워드
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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.
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참고문헌 (17)
참고문헌 신청
/ 1983 / The Dirichlet problem at innity of negative curvature 18 : 701 ~ 721
/ 1985 / Positive harmonic functions on complete mani-folds of negative curvature 121 : 429 ~ 461
/ 1994 / Convexity at innity and Brownian motion on manifolds with unboundednegative curvature : 189 ~ 220
D. Sullivan / 1983 / The Dirichlet problem at innity for a negatively curved manifold 18 : 723 ~ 732
E. P. Hsu / 2003 / Brownian motion and Dirichlet problems at innity 31 (3) : 1305 ~ 1319
/ 1985 / Positive harmonic functions on complete mani-folds of negative curvature 121 : 429 ~ 461
/ 1994 / Convexity at innity and Brownian motion on manifolds with unboundednegative curvature : 189 ~ 220
D. Sullivan / 1983 / The Dirichlet problem at innity for a negatively curved manifold 18 : 723 ~ 732
E. P. Hsu / 2003 / Brownian motion and Dirichlet problems at innity 31 (3) : 1305 ~ 1319
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