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arXiv · 1310.3666

Local gauge conditions for ellipticity in conformal geometry

Tony Liimatainen·Mikko Salo
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Abstract

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.

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Tony Liimatainen, Mikko Salo. 2013-10-14. Local gauge conditions for ellipticity in conformal geometry. https://arxiv.org/abs/1310.3666

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