scholarly journals A Bochner formula for harmonic maps into non-positively curved metric spaces

2019 ◽  
Vol 58 (4) ◽  
Author(s):  
Brian Freidin
Keyword(s):  
Metric Spaces ◽  
Harmonic Maps ◽  
Bochner Formula ◽  
Positively Curved

scholarly journals UNIQUENESS THEOREMS FOR HARMONIC MAPS INTO METRIC SPACES

2002 ◽  
Vol 04 (04) ◽  
pp. 725-750 ◽  
Author(s):  
CHIKAKO MESE
Keyword(s):  
Riemannian Manifolds ◽  
Metric Space ◽  
Metric Spaces ◽  
Harmonic Maps ◽  
Uniqueness Theorems ◽  
Singular Spaces ◽  
Domain Space ◽  
Recent Developments

Recent developments extend much of the known theory of classical harmonic maps between smooth Riemannian manifolds to the case when the target is a metric space of curvature bounded from above. In particular, the existence and regularity theorems for harmonic maps into these singular spaces have been successfully generalized. Furthermore, the uniqueness of harmonic maps is known when the domain has a boundary (with a smallness of image condition if the target curvature is bounded from above by a positive number). In this paper, we will address the question of uniqueness when the domain space is without a boundary in two cases: one, when the curvature of the target is strictly negative and two, for a map between surfaces with nonpositive target curvature.

scholarly journals Harmonic maps and a pinching theorem for positively curved hypersurfaces

1987 ◽  
Vol 99 (1) ◽  
pp. 182-182
Author(s):  
H. S. Hu ◽  
Y. L. Pan ◽  
Y. B. Shen
Keyword(s):  
Harmonic Maps ◽  
Positively Curved

Constancy of p-harmonic maps of finite q-energy into non-positively curved manifolds

2007 ◽  
Vol 258 (2) ◽  
pp. 347-362 ◽  
Author(s):  
Stefano Pigola ◽  
Marco Rigoli ◽  
Alberto G. Setti
Keyword(s):  
Harmonic Maps ◽  
Curved Manifolds ◽  
Positively Curved
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