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pro vyhledávání: '"Sutton, Craig"'
Let a torus $T$ act freely on a closed manifold $M$ of dimension at least two. We demonstrate that, for a generic $T$-invariant Riemannian metric $g$ on $M$, each real $\Delta_g$-eigenspace is an irreducible real representation of $T$ and, therefore,
Externí odkaz:
http://arxiv.org/abs/2207.14405
We continue our exploration of the extent to which the spectrum encodes the local geometry of a locally homogeneous three-manifold and find that if $(M,g)$ and $(N,h)$ are a pair of locally homogeneous, locally non-isometric isospectral three-manifol
Externí odkaz:
http://arxiv.org/abs/1910.14118
Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we explore the ex
Externí odkaz:
http://arxiv.org/abs/1905.11454
Autor:
Sutton, Craig J.
Intuition drawn from quantum mechanics and geometric optics raises the following long-standing question: can the length spectrum of a closed Riemannian manifold be recovered from its Laplace spectrum? The Poisson relation states that for any closed R
Externí odkaz:
http://arxiv.org/abs/1606.07426
Akademický článek
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A result of Bangert states that the stable norm associated to any Riemannian metric on the $2$-torus $T^2$ is strictly convex. We demonstrate that the space of stable norms associated to metrics on $T^2$ forms a proper dense subset of the space of st
Externí odkaz:
http://arxiv.org/abs/1010.1265
The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we demonstrated that the
Externí odkaz:
http://arxiv.org/abs/1006.5414
In 2004, Sormani and Wei introduced the covering spectrum: a geometric invariant that isolates part of the length spectrum of a Riemannian manifold. In their paper they observed that certain Sunada isospectral manifolds share the same covering spectr
Externí odkaz:
http://arxiv.org/abs/0905.0380
Publikováno v:
Ann. Inst. Fourier 60 (2010), no. 5, 1617-1628
We show that a bi-invariant metric on a compact connected Lie group $G$ is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric $g_0$ on $G$ there is a positive integer $N$ such that, with
Externí odkaz:
http://arxiv.org/abs/0710.2911
Autor:
Gordon, Carolyn S., Sutton, Craig J.
We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symme
Externí odkaz:
http://arxiv.org/abs/0707.0853