NSF Award
0604638
Abstract<br/><br/>Award: DMS-0604638<br/>Principal Investigator: Wenxiong Chen<br/><br/>The principal investigator will work on a series of nonlinear<br/>partial differential equations, integral equations and systems,<br/>as well as other nonlinear problems. Most of the problems arise<br/>from differential or convex geometry, such as the semi-linear<br/>elliptic equations from prescribing Gaussian and scalar curvature<br/>and the Monge-Ampere equations from the well-known Lp- Minkowski<br/>problem.<br/><br/>According to Einstein, the Universe we lived in is a curved<br/>space, in which gravity is realized as a distortion or bending of<br/>space-time in the neighborhood of a massive object and this<br/>change of shape is measured by curvature. One of these projects is focused <br/>on understanding when a given function can<br/>become a curvature. This is a challenging problem in global<br/>analysis and has interesting consequences in Riemannian Geometry.<br/>The other of the PI's major projects, the Lp Minkowski problem,<br/>is the central question of the Brunn-Minkowski Theory, which is<br/>the very core of Convex Geometric Analysis. Results in this area<br/>have been applied to numerous disciplines, including stereology,<br/>stochastic geometry, integral geometry, number theory,<br/>combinatorics, probability, statistics, and information theory.<br/>The nonlinear partial differential equations and integral<br/>equations and systems studied in this project also have various<br/>applications in physics, chemistry, and biology. One example is a<br/>modeling of chemical reaction in rivers or in blood streams,<br/>which would provide useful information in controlling pollution<br/>in rivers.
