Zobrazeno 1 - 10
of 819
pro vyhledávání: '"58C40"'
In 1964, John Milnor, using a construction of two lattices by Witt, produced the first example of two flat tori that are not globally isometric and whose Laplacians for exterior forms have the same sequence of eigenvalues. The aforementioned flat tor
Externí odkaz:
http://arxiv.org/abs/2412.16709
Autor:
Wang, Xing, Zhang, Cheng
On smooth compact manifolds with smooth boundary, we first establish the sharp lower bounds for the restrictions of harmonic functions in terms of their frequency functions, by using a combination of microlocal analysis and frequency function techniq
Externí odkaz:
http://arxiv.org/abs/2412.13955
We extend the buckling and clamped-plate problems to the context of differential forms on compact Riemannian manifolds with smooth boundary. We characterize their smallest eigenvalues and prove that, in the case of Euclidean domains, their spectra on
Externí odkaz:
http://arxiv.org/abs/2412.05612
We prove that the Patterson-Sullivan and Wigner distributions on the unit sphere bundle of a convex-cocompact hyperbolic surface are asymptotically identical. This generalizes results in the compact case by Anantharaman-Zelditch and Hansen-Hilgert-Sc
Externí odkaz:
http://arxiv.org/abs/2411.19782
Autor:
Lam, Hy
In this paper, we establish the spectral decomposition of the Koopman operator and determine the flat-trace distribution associated with the geodesic flow on the co-circle bundle over the compactification of Poincar\'e upper half-plane $\mathbf{H}^2
Externí odkaz:
http://arxiv.org/abs/2411.11392
The action of the subgroup $\operatorname{G}_2$ of $\operatorname{SO}(7)$ (resp.\ $\operatorname{Spin}(7)$ of $\operatorname{SO}(8)$) on the Grassmannian space $M=\frac{\operatorname{SO}(7)}{\operatorname{SO}(5)\times\operatorname{SO}(2)}$ (resp.\ $M
Externí odkaz:
http://arxiv.org/abs/2411.06886
Autor:
Lo, Chia-Chun
We show that the spectrum of a Schr\"odinger eigenvalue problem posed on a closed Riemannian manifold $M$ with non-negative potential can be approached by that of Robin eigenvalue problems with constant positive boundary parameter posed on a sequence
Externí odkaz:
http://arxiv.org/abs/2411.01594
Autor:
Denson, Jacob
For any bounded, regulated function $m: [0,\infty) \to \mathbb{C}$, consider the family of operators $\{ T_R \}$ on the sphere $S^d$ such that $T_R f = m(k/R) f$ for any spherical harmonic $f$ of degree $k$. We completely characterize the compactly s
Externí odkaz:
http://arxiv.org/abs/2410.23505
Autor:
Dietze, Charlotte, Read, Larry
We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter regime, we id
Externí odkaz:
http://arxiv.org/abs/2410.20563
Autor:
Deleporte, Alix, Rouveyrol, Marc
This article is a continuation of arXiv:2401.14977. We study the concentration properties of spectral projectors on manifolds, in connection with the uncertainty principle. In arXiv:2401.14977, the second author proved an optimal uncertainty principl
Externí odkaz:
http://arxiv.org/abs/2410.01323