Hyperbolic triangles without embedded eigenvalues
نویسندگان
چکیده
منابع مشابه
Dirichlet eigenvalues of asymptotically flat triangles
This paper is devoted to the study of the eigenpairs of the Dirichlet Laplacian on a family of triangles where two vertices are fixed and the altitude associated with the third vertex goes to zero. We investigate the dependence of the eigenvalues on this altitude. For the first eigenvalues and eigenfunctions, we obtain an asymptotic expansion at any order at the scale cube root of this altitude...
متن کاملHyperbolic Knot Complements without Closed Embedded Totally Geodesic Surfaces
It is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces can ...
متن کاملFibonacci words in hyperbolic Pascal triangles
The hyperbolic Pascal triangle HPT 4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of HPT 4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the h...
متن کاملPascal’s Triangles in Abelian and Hyperbolic Groups
We are used to imagining Pascal’s triangle as extending forever downwards from a vertex located at the top. But it is interesting to see it as occupying the first quadrant of the plane with it’s vertex at (0, 0). Imagine further that the plane is made of graph paper — that is, that we have embedded into it the Cayley graph of Z × Z with respect to the standard generating set. If we place the en...
متن کاملHydrodynamic stability without eigenvalues.
Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2018
ISSN: 0003-486X
DOI: 10.4007/annals.2018.187.2.1