Mónica Clapp (Instituto de Matemáticas-UNAM, Mexico)
New blow up profiles for Yamabe type problems
Abstract: Many problems in differential geometry are expressed in terms of an elliptic partial differential equation which is conformally invariant. Typical examples are the Yamabe problem or the prescribed scalar curvature problem.
The invariance of these equations under dilations gives rise to blow-up phenomena, which makes them hard to solve. It is, thus, important to understand these phenomena, in other words, to obtain information on energy level, the location and the limit profile of the blow-up.
A particular profile has been profusely studied: that given by the so-called standard bubble, i.e., the solution to the Yamabe problem on the round sphere. It has been successfully used to construct solutions of many different types of problems.
In this talk we will exhibit other blow-up profiles, which arise by considering special types of symmetries, and we will use them to produce solutions of some elliptic PDEs.
Temas: