Geometry driven type II higher dimensional blow-up for the critical heat equation

We consider the problem v_t=Δv+|v|^p−1vin Ω×(0,T),v=0on ∂Ω×(0,T),v>0in Ω×(0,T). In a domain Ω⊂R^d, d≥7 enjoying special symmetries, we find the first example of a solution with type II blow-up for a power p less than the Joseph-Lundgren exponent [Formula presented] No type II radial blow-up is present for p<p_JL(d). We take [Formula presented], the Sobolev critical exponent in one dimension less. The solution blows up on circle contained in a negatively curved part of the boundary in the form of a sharply scaled Aubin-Talenti bubble, approaching its energy density a Dirac measure for the curve. This is a completely new phenomenon for a diffusion setting.