Zobrazeno 1 - 10
of 6 095
pro vyhledávání: '"Kennedy,James"'
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