Prescribing the $ Q' $-curvature in three dimension

Pak Tung Ho

doi:10.3934/dcds.2019096

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2019, Volume 39, Issue 4: 2285-2294. Doi: 10.3934/dcds.2019096

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Prescribing the $ Q' $-curvature in three dimension

Pak Tung Ho

Department of Mathematics, Sogang University, Seoul 121-742, Korea

Received: August 31, 2018

Revised: September 30, 2018

Published: January 2019

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Abstract

In this note, we consider the problem of prescribing $ \overline{Q}' $-curvature on a three-dimensional pseudohermitian manifold. Given a positive CR pluriharmonic function $ f $, we construct a contact form on the three-dimensional pseudo-Einstein manifold with $ \overline{Q}' $-curvature being equal to $ f $, under some natural positivity conditions. On the other hand, we prove a Kazdan-Warner type identity for the problem of prescribing $ \overline{Q}' $-curvature on the standard CR three sphere.

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Mathematics Subject Classification: Primary: 32V20, 53A30; Secondary: 35R01, 53D10.

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