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CR-HARMONIC MAPS

Published online by Cambridge University Press:  02 December 2019

GAUTIER DIETRICH Open the ORCID record for GAUTIER DIETRICH [Opens in a new window]
GAUTIER DIETRICH*
Affiliation:
Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Case courrier 051, Place Eugène Bataillon, 34090Montpellier, FranceUniversité Paul-Valéry Montpellier 3 email gautier.dietrich@ac-montpellier.fr
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Abstract

We develop the notion of renormalized energy in Cauchy–Riemann (CR) geometry for maps from a strictly pseudoconvex pseudo-Hermitian manifold to a Riemannian manifold. This energy is a CR invariant functional whose critical points, which we call CR-harmonic maps, satisfy a CR covariant partial differential equation. The corresponding operator coincides on functions with the CR Paneitz operator.

Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 222 - 242
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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Footnotes

The author was supported in part by the grant ANR-17-CE40-0034 of the French National Research Agency ANR (project CCEM).

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