TY - JOUR
T1 - The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets
JO - Analysis in Theory and Applications
VL - 4
SP - 374
EP - 386
PY - 2018
DA - 2018/11
SN - 34
DO - http://doi.org/10.4208/ata.OA-2017-0070
UR - https://global-sci.org/intro/article_detail/ata/12850.html
KW - Neumann Laplacian, ”hot spots” conjecture, homogeneous hierarchical gasket, spectral decimation, analysis on fractals.
AB - <p style="text-align: justify;">In this paper, using spectral decimation, we prove that the <span style="text-align: justify;">&quot;</span>hot spots&quot; conjecture
holds 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.&nbsp;</p>