Colloquium PaperNonlinear partial differential equations and applications: Some nonlinear elliptic equations from geometry

摘要

We describe some recent work on certain nonlinear elliptic equations from geometry. These include the problem of prescribing scalar curvature on 𝕊ⁿ, the Yamabe problem on manifolds with boundary, and the best Sobolev inequality on Riemannian manifolds.