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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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