Geometric Analysis and PDEs

Matthew J. Gursky, Ermanno Lanconelli, Andrea Malchiodi, Gabriella Tarantello, Xu-Jia Wang, Paul C. Yang (auth.), Sun-Yung Alice Chang, Antonio Ambrosetti, Andrea Malchiodi (eds.)9783642016738, 9783642016745, 3642016731

This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.

Table of contents :
Front Matter….Pages 1-12
PDEs in Conformal Geometry….Pages 1-33
Heat Kernels in Sub-Riemannian Settings….Pages 35-61
Concentration of Solutions for Some Singularly Perturbed Neumann Problems….Pages 63-115
On Some Elliptic Problems in the Study of Selfdual Chern-Simons Vortices….Pages 117-175
The k-Hessian Equation….Pages 177-252
Minimal Surfaces in CR Geometry….Pages 253-273
Back Matter….Pages 1-14