Geometric Analysis

Geometric analysis is about the study of problems that are amenable to both analytic and geometric methods. For example many problems in geometry

can be formulated as variational problems or as problems about systems of partial differential equations, and in the other direction, important

information about solutions to variational problems or systems of partial differential equations can be obtained from knowledge about the

underlying geometry.

 

Current research interests in this area include:

(a) the Morse-Sard Theorem and related results in the context of Sobolev mappings

(b) existence/regularity theory for mappings between manifolds that minimize variational integrals

(c) non-linear Yamabe problem which seeks for metrics with certain curvature property in a fixed conformal class of metrics

(d) maximal (hyper)surfaces in Lorentzian manifolds

(e) soliton-like solutions arising from general relativity and geometrical flows

(f) Nonlinear wave equations via geometric approaches and mathematical relativity

 

Faculty: Jan Kristensen, Qian WangLuc Nguyen and Melanie Rupflin

Students: Syafiq Johar