The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets (Analysis in Theory and Applications, 2018)
In this paper, using spectral decimation, we prove that the "hot spots" conjectureholds on a class of homogeneous hierarchical gaskets introduced by Hambly,i.e., every eigenfunction of the second-smallest eigenvalue of the Neumann Laplacian(introduced by Kigami) attains its maximum and minimum on the boundary.
Keywords: Neumann Laplacian; ”hot spots” conjecture; homogeneous hierarchical gasket; spectral decimation; analysis on fractals.