Principal Investigator: Wenxiong Chen
The principal investigator will work on a series of nonlinear partial differential equations, integral equations and systems, as well as other nonlinear problems. Most of the problems arise from differential or convex geometry, such as the semi-linear elliptic equations from prescribing Gaussian and scalar curvature and the Monge-Ampere equations from the well-known Lp- Minkowski problem.
According to Einstein, the Universe we lived in is a curved space, in which gravity is realized as a distortion or bending of space-time in the neighborhood of a massive object and this change of shape is measured by curvature. One of these projects is focused on understanding when a given function can become a curvature. This is a challenging problem in global analysis and has interesting consequences in Riemannian Geometry. The other of the PI's major projects, the Lp Minkowski problem, is the central question of the Brunn-Minkowski Theory, which is the very core of Convex Geometric Analysis. Results in this area have been applied to numerous disciplines, including stereology, stochastic geometry, integral geometry, number theory, combinatorics, probability, statistics, and information theory. The nonlinear partial differential equations and integral equations and systems studied in this project also have various applications in physics, chemistry, and biology. One example is a modeling of chemical reaction in rivers or in blood streams, which would provide useful information in controlling pollution in rivers.
