Local Gauge Conditions for Ellipticity in Conformal Geometry
Liimatainen, T., & Salo, M. (2016). Local Gauge Conditions for Ellipticity in Conformal Geometry. International Mathematics Research Notices, 2016(13), 4058-4077. https://doi.org/10.1093/imrn/rnv255
Published inInternational Mathematics Research Notices
© The Author(s) 2015. This is a final draft version of an article whose final and definitive form has been published by Oxford University Press. Published in this repository with the kind permission of the publisher.
In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an n-harmonic coordinate system and normalizing the determinant of the metric. We also give corresponding elliptic regularity results and characterizations of local conformal flatness in low regularity settings.
PublisherOxford University Press
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