Nonlinear Equations in Conformal Geometry

posted Jul 9, 2010, 10:24 AM by Glenna Buford

Sun-Yung Alice Chang
Princeton University and the University of California, Los Angeles

AWM Emmy Noether Lecture
Thursday, January 11, 2001
9:00 a.m. - 9:50 a.m. 
Ballrooms ABC, 5th Floor, Sheraton New Orleans Hotel
New Orleans, Louisiana

Abstract. Elliptic equations have been and continue to be an important tool in the study of problems in geometry. In recent decades, non-linear second order elliptic equations with critical exponents have played a special role in the solutions of several important problems in conformal geometry; e.g. the problem of prescribing Gaussian curvature and the Yamabe problem. In this talk, I will describe some recent efforts to extend the role played by second order semilinear equations to higher order semilinear equations as well as second order fully non-linear equations. A common feature essential to understanding such equations is the analysis of blow up in these equations. This analysis involves classifying entire solutions to such equations in Euclidean space. I plan to discuss examples of blowup phenomena in several such situations.