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A RIGIDITY PROPERTY OF PLURIHARMONIC MAPS FROM PROJECTIVE MANIFOLDS

Part of: Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  13 October 2022

CHE-HUNG HUANG Open the ORCID record for CHE-HUNG HUANG [Opens in a new window]
CHE-HUNG HUANG*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
*
e-mail: [email protected]
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Abstract

Suppose M is a complex projective manifold of dimension $\geq 2$, V is the support of an ample divisor in M and U is an open set in M that intersects each irreducible component of V. We show that a pluriharmonic map $f:M\to N$ into a Kähler manifold N is holomorphic whenever $f\vert _{V\,\cap \, U}$ is holomorphic.

Keywords

harmonic mappings

MSC classification

Primary: 58E20: Harmonic maps , etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 1 , August 2023 , pp. 166 - 168
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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