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Finite total $Q$-curvature on a locally conformally flat manifold

Connections for Women: Differential Geometry January 14, 2016 - January 15, 2016

January 15, 2016 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Yi Wang (Johns Hopkins University)
Location: MSRI: Simons Auditorium
Tags/Keywords
• differential geometry

• Manifolds

• curvature

• geodesic flow

• Q-curvature

• integral geometry

• Gaussian curvature

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14417

Abstract

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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