6533b82afe1ef96bd128b779

RESEARCH PRODUCT

Local Gauge Conditions for Ellipticity in Conformal Geometry

Mikko SaloTony Liimatainen

subject

Mathematics - Differential Geometry53A30 (Primary) 53B20 35J60 (Secondary)General MathematicsCoordinate systemConformal mapCurvatureconformal geometry01 natural sciencessymbols.namesakeMathematics - Analysis of PDEs0103 physical sciencesFOS: Mathematics0101 mathematicsFlatness (mathematics)Mathematics010308 nuclear & particles physicsta111010102 general mathematicsMathematical analysisgauge conditionsGauge (firearms)Elliptic operatorDifferential Geometry (math.DG)symbolsWeyl transformationMathematics::Differential GeometryConformal geometryAnalysis of PDEs (math.AP)curvature tensors

description

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.

yearjournalcountryeditionlanguage
2013-10-14
http://urn.fi/URN:NBN:fi:jyu-201611184672