Conformal differential geometry of a subspace

1 Overdetermined Systems , Conformal Differential Geometry , and the Bgg Complex

This is an expanded version of a series of two lectures given at the IMA summer program “Symmetries and Overdetermined Systems of Partial Differential Equations”. The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined system obtained recently in joint work with T.P. Branson, M.G. Eastwood, and A.R. Gover. First a simple special cas...

Conformal Geometry

Arrows in this diagram indicate input from one topic to another. Closely related topics are joined by lines. Conformal geometry is highly analogous to CR geometry, so their boxes are close together and arrows run in both directions. The left hand side of the diagram is largely algebraic. At the top of the diagram, Q-curvature and ambient metrics are specific aspects of conformal geometry, which...

Overdetermined systems, conformal differential geometry, and the BGG complex

This is an expanded version of a series of two lectures given at the IMA summer program “Symmetries and Overdetermined Systems of Partial Differential Equations”. The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined system obtained recently in joint work with T.P. Branson, M.G. Eastwood, and A.R. Gover. First a simple special cas...

Non-linear Partial Differential Equations in Conformal Geometry

In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformal Laplacian, and their associated conformal invariants have been introduced. The conformally covariant powers of the La...

Conformal Random Geometry