Concentration Lemma

Abstract

In this chapter we show that the mass quantization of collapse occurs if the solution blows up in infinite time [148]. It is uncertain whether such a solution exists or not. Actually, it is suspected that the blowup in infinite time occurs only when the solution converges to a singular stationary solution, and therefore, in that case, the total mass λ = ||uO||₁ must be quantized as λ ∈ 4πN. This question is open, but an important tool is exploited, which we call the concentration lemma. (This is different from the lemma given by [23].)