Crossing New Frontiers in Mathematics and Science
Geometric analysis is of great importance because of its interaction with other mathematical and scientific disciplines. The nature of geometry often forces scientists, such as Dr. Pengfei Guan, to search for "special" solutions. Each geometric fully nonlinear equation has a special structure with different consequences in geometry. Thus these equations pose challenging questions in nonlinear partial differential equations and point out new directions in geometric analysis.
The main focus of Dr. Guan's research is the study of geometric elliptic and parabolic fully nonlinear partial differential equations arising in differential geometry. Dr. Guan has made several important breakthroughs on some longstanding problems in geometric analysis and his work crosses mathematical frontiers. As the holder of a Canada Research Chair in Geometric Analysis, he continues to develop analytic tools for various mathematical equations and investigate structures of geometric solutions, among other related topics.
The advances being made by Dr. Guan in the theory of these equations is leading to the solutions of important problems in geometry and enriching the existing theory of fully nonlinear partial differential equations in general. In the process, his work is having important consequences in both physics and applied sciences.