Zobrazeno 1 - 10
of 1 111
pro vyhledávání: '"Steklov eigenvalues"'
Autor:
He, Fei, Wang, Lihan
We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be viewed as a weakened version of P\'{o}lya's Conjecture in the Steklov ca
Externí odkaz:
http://arxiv.org/abs/2411.07566
Let $\Delta$ and $B$ be the maximum vertex degree and a subset of vertices in a graph $G$ respectively. In this paper, we study the first (non-trivial) Steklov eigenvalue $\sigma_2$ of $G$ with boundary $B$. Using metrical deformation via flows, we f
Externí odkaz:
http://arxiv.org/abs/2410.22632
We obtain geometric lower bounds for the low Steklov eigenvalues of finite-volume hyperbolic surfaces with geodesic boundary. The bounds we obtain depend on the length of a shortest multi-geodesic disconnecting the surfaces into connected components
Externí odkaz:
http://arxiv.org/abs/2408.04534
Autor:
Selutckii, Denis
In this paper we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that in some cases this boundary is sharp.
Externí odkaz:
http://arxiv.org/abs/2407.13422
Autor:
Brisson, Jade, Colbois, Bruno
In this note, we investigate the Steklov spectrum of the warped product $[0,L]\times_h \Sigma$ equipped with the metric $dt^2+h(t)^2g_\Sigma$, where $\Sigma$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the
Externí odkaz:
http://arxiv.org/abs/2403.13620
Autor:
Mao, Jing, Zhang, Shijie
In this paper, by imposing suitable assumptions on the weighted function, (under the constraint of fixed weighted volume) a Brock-type isoperimetric inequality for Steklov-type eigenvalues of the Witten-Laplacian on bounded domains in a Euclidean spa
Externí odkaz:
http://arxiv.org/abs/2404.07412
We investigate upper bounds for the spectral ratios and gaps for the Steklov eigenvalues of balls with revolution-type metrics. We do not impose conditions on the Ricci curvature or on the convexity of the boundary. We obtain optimal upper bounds for
Externí odkaz:
http://arxiv.org/abs/2403.13426
In this note we establish an expression for the Steklov spectrum of warped products in terms of auxiliary Steklov problems for drift Laplacians with weight induced by the warping factor. As an application, we show that a compact manifold with connect
Externí odkaz:
http://arxiv.org/abs/2403.08925
Autor:
Métras, Antoine, Tschanz, Léonard
Publikováno v:
Experimental Mathematics, 1 (2024)
We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space. In a recent article, the phenomenon of critical length, at which a Steklov eigenvalue is maximized, was exhibited and multiple questions were
Externí odkaz:
http://arxiv.org/abs/2401.10743
We consider the Steklov eigenvalue problem on a compact pinched negatively curved manifold $M$ of dimension at least three with totally geodesic boundaries. We obtain a geometric lower bound for the first nonzero Steklov eigenvalue in terms of the to
Externí odkaz:
http://arxiv.org/abs/2312.12180