Convex functions and harmonic maps
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- by William B. Gordon PDF
- Proc. Amer. Math. Soc. 33 (1972), 433-437 Request permission
Abstract:
A subset D of a riemannian manifold Y is said to be convex supporting if every compact subset of D has a Y-open neighborhood which supports a strictly convex function. The image of a harmonic map f from a compact manifold X to Y cannot be contained in any convex supporting subset of Y unless f is constant. Also, if Y has a convex supporting covering space and ${\pi _1}(X)$ is finite then every harmonic map from X to Y is necessarily constant. Examples of convex supporting domains and manifolds are given.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 433-437
- MSC: Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291987-1
- MathSciNet review: 0291987