Can one observe the bottleneckness of a space by the heat distribution?
Автор: Ishiwata Satoshi
Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu
Рубрика: Математика
Статья в выпуске: 3 (40), 2017 года.
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In this paper we discuss a bottleneck structure of a non-compact manifold appearing in the behavior of the heat kernel. This is regarded as an inverse problem of heat kernel estimates on manifolds with ends obtained in [10] and [8]. As a result, if a non-parabolic manifold is divided into two domains by a partition and we have suitable heat kernel estimates between different domains, we obtain an upper bound of the capacity growth of δ-skin of the partition. By this estimate of the capacity, we obtain an upper bound of the first non-zero Neumann eigenvalue of Laplace - Beltrami operator on balls. Under the assumption of an isoperimetric inequality, an upper bound of the volume growth of the δ-skin of the partition is also obtained.
Heat kernel, manifold with ends, inverse problem
Короткий адрес: https://sciup.org/14968911
IDR: 14968911 | DOI: 10.15688/mpcm.jvolsu.2017.3.6
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