Jeffrey Case, Penn State

Title: Conformally covariant polydifferential operators

Abstract: Conformally covariant differential operators, including the Yamabe operator, feature heavily in studies of the scalar and Q-curvatures as well as in (sharp) Sobolev inequalities. In this talk, I discuss multilinear analogues of these operators, known as conformally covariant polydifferential operators. In one direction, I show that these operators are ubiquitous; for example, there is such an operator associated to each variational scalar Riemannian invariant. In another direction, I describe a general approach to classifying local minimizers of a related Sobolev quotient. This talk is partially based on joint work with Yueh-Ju Lin and Wei Yuan.