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The
$L^{p}$ spectrum and heat dynamics of locally symmetric spaces of higher rank
Published online by Cambridge University Press: 30 June 2014
Abstract
The aim of this paper is to study the spectrum of the $L^{p}$ Laplacian and the dynamics of the
$L^{p}$ heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the
$L^{p}$ heat semigroup on
$M$ has a certain chaotic behavior if
$p\in (1,2)$, whereas for
$p\geq 2$ such chaotic behavior never occurs.
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- Research Article
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- © Cambridge University Press, 2014
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