Abstract
In this paper, we show a compactness criterion for contact forms in a fixed CR structure(i.e., conformal pseudohermitian structures), assuming a volume bound and L p bounds, p>2, on the Tanaka-Webster curvature, the pseudohermitian torsion and its covariant derivative. We also need the L 2 bound on the derivative of the Tanaka-Webster curvature along the characteristic vector field. As an application, we can show that the CR automorphism group is compact if M is not CR spherical or the CR Yamabe constant is negative.
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Chiu, HL. Compactness of pseudohermitian structures with integral bounds on curvature. Math. Ann. 334, 111–142 (2006). https://doi.org/10.1007/s00208-005-0709-4
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DOI: https://doi.org/10.1007/s00208-005-0709-4