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In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
In this article we study the positivity of the 4-th order Paneitz operator
for closed 3-manifolds. We prove that the connected sum of two such
3-manifold retains the same positivity property. We also solve the
analogue of the Yamabe equation for such a manifold.
We prove that the Paneitz energy on the standard three-sphere is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
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