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Yueh-Ju Lin "Deformations of Q-curvature."
Start Date: 4/16/2018Start Time: 4:00 PM
End Date: 4/16/2018End Time: 5:00 PM
Event Description:
Speaker: Yueh-Ju Lin, (Princeton)

Abstract: Stability (local surjectivity) and rigidity of the scalar curvature have been studied in an early work of Fischer-Marsden on ``vacuum static spaces''. Inspired by this line of research, we seek similar properties for Q-curvature by studying ``Q-singular spaces'', which were introduced by Chang-Gursky-Yang. In this talk, we investigate deformation problems of $Q$-curvature on closed Riemannian manifolds with dimensions $n\geq 3$. In particular, we prove local surjectivity for non-$Q$-singular spaces and local rigidity of flat manifolds. For global results, we show that any smooth functions can be realized as a $Q$-curvature on generic $Q$-flat manifolds. However, a locally conformally flat metric on $n$-tori with nonnegative $Q$-curvature has to be flat. This is joint work with Wei Yuan.
Location Information:
Homewood - Shaffer
Room: 303
Mathematics Department
Analysis/PDE Seminar

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