Zobrazeno 1 - 10
of 130
pro vyhledávání: '"Kennedy, James B."'
Autor:
Kennedy, James B., Rohleder, Jonathan
We prove a strong form of the hot spots conjecture for a class of domains in $\mathbb{R}^d$ which are a natural generalization of the lip domains of Atar and Burdzy [J. Amer. Math. Soc. 17 (2004), 243-265] in dimension two, as well as for a class of
Externí odkaz:
http://arxiv.org/abs/2410.00816
We examine diagonal combs, a recently identified class of infinite metric graphs whose properties depend on one parameter. These graphs exhibit a fascinating regime where they possess infinite volume while maintaining purely discrete spectrum for the
Externí odkaz:
http://arxiv.org/abs/2403.10708
We study the problem of minimizing or maximizing the fundamental spectral gap of Schr\"odinger operators on metric graphs with either a convex potential or a ``single-well'' potential on an appropriate specified subset. (In the case of metric trees,
Externí odkaz:
http://arxiv.org/abs/2401.04344
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of the spectra
Externí odkaz:
http://arxiv.org/abs/2312.04952
Autor:
Kennedy, James B., Ribeiro, João P.
We study partition problems based on two ostensibly different kinds of energy functionals defined on $k$-partitions of metric graphs: Cheeger-type functionals whose minimisers are the $k$-Cheeger cuts of the graph, and the corresponding values are th
Externí odkaz:
http://arxiv.org/abs/2310.02701
Autor:
Freitas, Pedro, Kennedy, James B.
Inspired by a recent result of Funano's, we provide a sharp quantitative comparison result between the first nontrivial eigenvalues of the Neumann Laplacian on bounded convex domains $\Omega_{1} \subset \Omega_{2}$ in any dimension $d$ greater than o
Externí odkaz:
http://arxiv.org/abs/2307.06593
We investigate the existence or non-existence of spectral minimal partitions of unbounded metric graphs, where the operator applied to each of the partition elements is a Schr\"odinger operator of the form $-\Delta + V$ with suitable (electric) poten
Externí odkaz:
http://arxiv.org/abs/2209.03658
We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called Friedrichs and Neumann extensions. We introduce a new criterion for co
Externí odkaz:
http://arxiv.org/abs/2207.04024
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total length of t
Externí odkaz:
http://arxiv.org/abs/2206.10046
Autor:
Buoso, Davide, Kennedy, James B.
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its eigenvalue
Externí odkaz:
http://arxiv.org/abs/2105.11249