Local gauge conditions for ellipticity in conformal geometry
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🧮 math.DG
math.AP
keywords
conditionsconformalgaugelocalellipticgeometryregularitytensors
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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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