Compactness-and-stability-for-solution-of-escobar-yamabe-problem

Abstract:

In 1992 Escobar extended the well known Yamabe problem to
manifolds with boundary, when the target manifold is scalar flat. This
problem, called Escobar-Yamabe, or Yamabe boundary problem is
particularly interesting since it also represents a generalization to
Riemann mapping theorem to higher dimensions.
In this talk we discuss when the solutions of this problem are a
compact set, or when they form a blowing up sequence. We will
underline the affinities and the differences with the classical Yamabe
problem.