In this talk, I will report some recent joint study with Gursky and Yang on the topic of conformal invariants on a Riemannanian manifold (M^n,g) equipped with a smooth measure m. In particular, we show that there is a natural definition of the Ricci and scalar curvatures associated to such a space, both of which are conformally invariant. We will compare this notion with that of Baker-Emery and G. Perelman. I will indicate methods to construct families of conformally covariant operators defined on these spaces. Certain variational problems in this setting are considered, including a generalization of the Einstein-Hibert action.

Lecture #12238

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 12238-12238-QuickTime.mov (500 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 12238-12238-DVD PCM Audio.aiff (738 MB - Audio Only)
• 12238-12238-MPEG-2 120min High Quality Encode.m2v (1683 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.