Title: Fully nonlinear PDEs in real and complex geometry and optics : Cetraro, Italy 2012 /
Authors: Capogna, Luca, 1966-; Gutiérrez, Cristian E., 1950-; Lanconelli, E.
Publisher: Springer,
Year: 2014
Subjects: Differential equations, Partial Congresses.; Differential equations, Nonlinear Congresses.; Teichmüller spaces Congresses.; Conformal mapping Congresses.; Monge-Ampère equations Congresses.; Conformal mapping; Differential equations, Nonlinear; Differential equations, Partial.; Monge-Ampère equations; Teichmüller spaces
Abstract: The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Guteirrez, and On the Levi Monge Ampère equation by Annamaria Montanari.
Contents: L[infinity symbol] extremal mappings in AMLE and Teichmüller theory / Luca Capogna -- Curvature measures, isoperimetric type inequalities and fully nonlinear PDEs / Pengfei Guan -- Refraction problems in geometric optics / Cristian E. Gutierez -- On the Levi Monge-Ampère equation / Annamaria Montanari.