This book covers recent advances in several important areas of geometric analysis including extremal eigenvalue problems, mini-max methods in minimal surfaces, CR geometry in dimension three, and the Ricci flow and Ricci limit spaces. An output of the CIME Summer School "Geometric Analysis" held in Cetraro in 2018, it offers a collection of lecture notes prepared by Ailana Fraser (UBC), André Neves (Chicago), Peter M. Topping (Warwick), and Paul C. Yang (Princeton).

These notes will be a valuable asset for researchers and advanced graduate students in geometric analysis.

Inhalt

• Extremal Eigenvalue Problems and Free Boundary Minimal Surfaces in the Ball. - Applications of Min-Max Methods to Geometry. - Ricci Flow and Ricci Limit Spaces. - Pseudo-Hermitian Geometry in 3D.