5/5/2005

Fengbo Hang
Michigan State University

Higher order conformal covariant operators on the sphere

The standard metric on the sphere minimizes the scaling invariant scalar curvature integral. This may be rewritten in terms of variational problems for conformal Laplacian operator and is equivalent to the classical sharp Sobolev inequality. We will discuss similar problems for the Q-curvature and 2mth order conformal covariant operator on the sphere, which was introduced by Graham-Jenne-Mason-Sparling and Branson. The case 2m>n (the dimension) is of particular interest since negative exponent appears.