The "Hot Spots" Conjecture For The Homogeneous Hierarchical Gaskets

Since "hot spots" conjecture was proposed by J.Rauch in1974,it led many scholars to have discussion on this conjecture for kinds of domains in Euclidean space. they have known that the conjecture is established in some case,however,it is not hold in some domain.But all above discussions are based on the Euclidean space.so we want to know whether the "hot sports" holds in other space-for example,the fractal set.The article [12]and[13] have proven that the conjecture is hold in Sierpinski gasket (SG for short)and3-level Sierpinski gasket (SG3for short).In this paper,we will use the spectrum decimation and the method in [12]and[13] to prove that "hot spot" conjecture also holds in Homogeneous Hierarchical gasket (HH(b) for short).