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WEAK GEODESIC RAYS IN THE SPACE OF KÄHLER POTENTIALS AND THE CLASS ${\mathcal{E}}(X,\unicode[STIX]{x1D714})$

Part of: Differential operators in several variables Global differential geometry Pluripotential theory

Published online by Cambridge University Press:  03 September 2015

Tamás Darvas
Tamás Darvas*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA ([email protected])
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Abstract

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Suppose that $(X,\unicode[STIX]{x1D714})$ is a compact Kähler manifold. In the present work we propose a construction for weak geodesic rays in the space of Kähler potentials that is tied together with properties of the class ${\mathcal{E}}(X,\unicode[STIX]{x1D714})$. As an application of our construction, we prove a characterization of ${\mathcal{E}}(X,\unicode[STIX]{x1D714})$ in terms of envelopes.

Keywords

complex Monge–Ampère equationsgeodesic raysfinite energy classes

MSC classification

Primary: 53C55: Hermitian and Kählerian manifolds
Secondary: 32W20: Complex Monge-Ampère operators 32U05: Plurisubharmonic functions and generalizations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 4 , September 2017 , pp. 837 - 858
Copyright
© Cambridge University Press 2015 

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