Blow up phenomena of mean field type equations

We constructed blow-up solutions of mean field type equations on “degenerate” surfaces, including flat torus and standard sphere in dimension two. More recently, we built the blow-up solutions of “mean field equation” on four dimensional standard sphere, basing on point configurations inherited from the dimension two. New progress towards the planar Neumann problem will also be mentioned, particularly the construction of boundary and interior bubble assemblies.

学术海报.pdf