The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets
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@Article{ATA-34-374,
author = {Xiaofen Qiu},
title = {The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets},
journal = {Analysis in Theory and Applications},
year = {2018},
volume = {34},
number = {4},
pages = {374--386},
abstract = {
In this paper, using spectral decimation, we prove that the "hot spots" 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.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0070}, url = {http://global-sci.org/intro/article_detail/ata/12850.html} }
TY - JOUR
T1 - The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets
AU - Xiaofen Qiu
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 -
In this paper, using spectral decimation, we prove that the "hot spots" 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.
Xiaofen Qiu. (2018). The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets.
Analysis in Theory and Applications. 34 (4).
374-386.
doi:10.4208/ata.OA-2017-0070
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