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Volume 34, Issue 4
The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets

Xiaofen Qiu

Anal. Theory Appl., 34 (2018), pp. 374-386.

Published online: 2018-11

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  • 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. 

  • AMS Subject Headings

52B10, 65D18, 68U05, 68U07

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COPYRIGHT: © Global Science Press

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@Article{ATA-34-374, author = {}, 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 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. (1970). 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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