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pro vyhledávání: '"58J50, 58J35"'
Minakshisundaram and Pleijel gave an asymptotic formula for the sum of squares of the pointwise values of the eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold, with eigenvalues less than a fixed number. Here, a general
Externí odkaz:
http://arxiv.org/abs/2312.07078
Autor:
Fischer, Veronique
In this paper, we obtain asymptotic formulae on nilmanifolds $\Gamma \backslash G$, wher $G$ is any stratified (or even graded) nilpotent Lie group equipped with a co-compact discrete subgroup $\Gamma$. We study especially the asymptotics related to
Externí odkaz:
http://arxiv.org/abs/2112.01246
Autor:
Avramidi, Ivan G.
Publikováno v:
Journal of Mathematical Physics 61, 032303 (2020)
We introduce and study new spectral invariant of two elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depends on both the eigenvalues and the eigensections of the operators, which is
Externí odkaz:
http://arxiv.org/abs/1909.09680
Publikováno v:
Duke Math. J. 167, no. 10 (2018), 1883-1950
We establish a Cheeger-Muller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all non-compact hyperbolic spaces of finite volume, but we do not assume that the metr
Externí odkaz:
http://arxiv.org/abs/1411.1105
Manifolds with fibered cusps are a class of complete noncompact Riemannian manifolds including all locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing d
Externí odkaz:
http://arxiv.org/abs/1410.8406
Autor:
Portegies, Jacobus W.
We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from heat kernels at a certain time from a finite number of points. Both this time and this number can be bounded in terms of the dimension, a lower bound
Externí odkaz:
http://arxiv.org/abs/1311.7568
We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that allows us to
Externí odkaz:
http://arxiv.org/abs/1206.6077
Autor:
Gilkey, P., Miatello, R. J.
We study the asymptotic behavior of the heat trace coefficients $a_n$ as n tends to infinity for the scalar Laplacian in the context of locally symmetric spaces. We show that if the Plancherel measure of a noncompact type symmetric space is polynomia
Externí odkaz:
http://arxiv.org/abs/1109.6228
Autor:
Rowlett, J. M.
Publikováno v:
Comm. in Anal. and Geom. 16, no. 4, (2008), 735 - 798
In this paper we define a new convergence called "asymptotically conic convergence" in which a smooth family of Riemannian metrics on a fixed compact manifold degenerate to a metric with isolated conic singularity. Our results are: convergence of the
Externí odkaz:
http://arxiv.org/abs/math/0701383
Autor:
Veronique Fischer
Publikováno v:
Fischer, V 2022, ' Asymptotics and zeta functions on compact nilmanifolds ', Journal des Mathematiques Pures et Appliquees, vol. 160, pp. 1-28 . https://doi.org/10.1016/j.matpur.2021.12.007
In this paper, we obtain asymptotic formulae on nilmanifolds $\Gamma \backslash G$, wher $G$ is any stratified (or even graded) nilpotent Lie group equipped with a co-compact discrete subgroup $\Gamma$. We study especially the asymptotics related to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1fbfa7e8eef17dbbd75e44ffad9c00c5
http://arxiv.org/abs/2112.01246
http://arxiv.org/abs/2112.01246