Finite total $Q$-curvature on a locally conformally flat manifold
Connections for Women: Differential Geometry January 14, 2016 - January 15, 2016
Location: MSRI: Simons Auditorium
differential geometry
Manifolds
curvature
geodesic flow
Q-curvature
integral geometry
Gaussian curvature
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C44 - Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
54A20 - Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
14417
In this talk, we will discuss locally conformally flat manifolds with finite total curvature.
We prove that for such a manifold, the integral of the $Q$-curvature
equals an integral multiple of a dimensional constant. This
shows a new aspect of the $Q$-curvature on noncompact complete
manifolds. It provides further evidence that $Q$-curvature controls
geometry as the Gaussian curvature does in two dimension on locally conformally flat manifolds
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14417
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14417.mp4
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