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, including special immersions such as minimal surfaces or Willmore surfaces.
(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
(g) Analytic and geometric properties of smooth and non-smooth spaces satisfying Ricci curvature lower bounds
(h) Isometric embedding problems and their applications
Faculty: Gui-Qiang G. Chen, Jan Kristensen, Jason Lotay, Andrea Mondino, Luc Nguyen, Melanie Rupflin and Qian Wang,
Postdoctoral Research Fellows: Clemens Saemann
DPhil Students: Izar Alonso Lorenzo, Alessandro Cucinotta, Francesco Fiorani, Alfred Holmes, John Hughes, Thibault Langlais, Dimitri Navarro, Isaac Wind Newell, Vanessa Ryborz, Federico Trinca and Christopher Wright