Abstract
Conformally invariant quantities are, namely, those remaining invariant under the conformal changes of metrics which stretch the length of vectors but preserve the angles between every pair of vectors. In this lecture, the speaker will discuss some partial differential equations arising from the study of conformally invariant quantities in Riemannian geometry.
A classical problem in this field is the Yamabe problem. It is to find on a compact Riemannian manifold a conformal metric which has constant scalar curvature. This is equivalent to solving a conformally invariant semi-linear partial differential equation. The speaker will first revisit the resolution of this problem, as well as results on compactness of the solution set. A fully nonlinear version of the Yamabe problem will then be discussed. The existence, compactness, and quantitative properties of their solutions will be described afterwards.
About the speaker
Prof Yanyan Li received his MS from the Institute of Systems Science, Academia Sinica in 1983 and his PhD from Courant Institute of Mathematical Sciences of New York University in 1988. He began his professional career at Princeton University as an instructor in 1988. In 1990, Prof Li was hired as an Assistant Professor by Rutgers University, where he is currently the Distinguished Professor.
Prof Li has wide research interests, and is a world top expert in the area of partial differential equations and geometric analysis. He is also well known for his research on composite materials.
Prof Li was a speaker of invited 45-minute talks in the International Congress of Mathematicians in 2002 and 2010, which was one of the highest honors in the mathematics community. He was also awarded the Rutgers Board of Trustees Research Fellowship for Scholarly Excellence in 1993. He was elected the Alfred P. Sloan Research Fellow and a member of inaugural class of fellows of the American Mathematical Society. Prof Li is on the editorial board of more than ten mathematics journals and has also become the editor-in-chief of Analysis in Theory and Applications since 2013.
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