Royden Decomposition for Harmonic Maps with Finite Total Energy

Yong Hah Lee

doi:10.1007/s00025-015-0503-x

Royden Decomposition for Harmonic Maps with Finite Total Energy

Yong Hah Lee

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove the harmonic map version of the Royden decomposition in the sense that given any bounded C¹-map f with finite total energy on a complete Riemannian manifold into a Cartan-Hadamard manifold, there exists a unique bounded harmonic map with finite total energy from the manifold into the Cartan-Hadamard manifold taking the same boundary value at each harmonic boundary point as that of f.

Original language	English
Pages (from-to)	687-692
Number of pages	6
Journal	Results in Mathematics
Volume	71
Issue number	3-4
DOIs	https://doi.org/10.1007/s00025-015-0503-x
State	Published - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2015, Springer Basel.

Keywords

53C43
58E20
Harmonic map
Royden decomposition
harmonic boundary

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10.1007/s00025-015-0503-x

Cite this

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AB - We prove the harmonic map version of the Royden decomposition in the sense that given any bounded C1-map f with finite total energy on a complete Riemannian manifold into a Cartan-Hadamard manifold, there exists a unique bounded harmonic map with finite total energy from the manifold into the Cartan-Hadamard manifold taking the same boundary value at each harmonic boundary point as that of f.

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KW - 58E20

KW - Harmonic map

KW - Royden decomposition

KW - harmonic boundary

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Royden Decomposition for Harmonic Maps with Finite Total Energy

Abstract

Bibliographical note

Keywords

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