Conformal Geometry
Prerequisiti
Prerequisites are Functional Analysis and Sobolev Spaces in Rn. It is useful some basic knowledge of elliptic regularity theory and of Differential Geometry, but there will be a recollection of some basic notions and results.
Master and Ph.D.
Programma
Brief review in Differential Geometry
Sobolev Spaces on Manifolds
Sobolev quotient on Rn
Yamabe problem
Nirenberg problem and prescription of scalar curvature
Obiettivi formativi
The aim of the course is to apply methods in functional analysis, calculus of variatons and elliptic theory to geometric problems, in particular with lack of compactness.
Riferimenti bibliografici
T. Aubin: Some nonlinear problems in Riemannian geometry. SMN, Springer, 1998.
E. Hebey, Sobolev spaces on Riemannian manifolds.
J. Lee - T. Parker, The Yamabe problem. Bull. Amer. Math. Soc., 1987.
A. Malchiodi Prescribing scalar curvature in conformal geometry, EMS Press, Berlin, 2023.