Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Canzani, Yaiza"'
A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal partitions coincide with nodal partitions of Courant-sharp Laplacian eige
Externí odkaz:
http://arxiv.org/abs/2406.04225
We obtain upper bounds on the number of nodal domains of Laplace eigenfunctions on chain domains with Neumann boundary conditions. The chain domains consist of a family of planar domains, with piecewise smooth boundary, that are joined by thin necks.
Externí odkaz:
http://arxiv.org/abs/2305.16452
Let $(M,g)$ be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold without boundary all of whose geodesics are closed with a minimal common period $T$. The positive definite Laplace-Beltrami operator has eigenvalues $\{\lambda_j^2\}_j$ whic
Externí odkaz:
http://arxiv.org/abs/2211.09644
Autor:
Canzani, Yaiza, Toth, John A.
Let $(M,g)$ be a compact, smooth Riemannian manifold and $\{u_h\}$ be a sequence of $L^2$-normalized Laplace eigenfunctions that has a localized defect measure $\mu$ in the sense that $ M \setminus \text{supp}(\pi_* \mu) \neq \emptyset$ where $\pi:T^
Externí odkaz:
http://arxiv.org/abs/2207.05607
Autor:
Canzani, Yaiza, Galkowski, Jeffrey
Let $M$ be a smooth compact manifold of dimension $d$ without boundary. We introduce the concept of predominance for Riemannian metrics on $M$, a notion analogous to full Lebesgue measure which, in particular, implies density. We show that for a pred
Externí odkaz:
http://arxiv.org/abs/2204.11921
Publikováno v:
Calc. Var. PDE 61 203 (2022)
The oscillation of a Laplacian eigenfunction gives a great deal of information about the manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, an important geometric quantity that is notoriously hard to compute, or
Externí odkaz:
http://arxiv.org/abs/2201.00773
Publikováno v:
Pure Appl. Analysis 4 (2022) 225-256
We prove quantitative norm bounds for a family of operators involving impedance boundary conditions on convex, polygonal domains. A robust numerical construction of Helmholtz scattering solutions in variable media via the Dirichlet-to-Neumann operato
Externí odkaz:
http://arxiv.org/abs/2103.14700
Autor:
Canzani, Yaiza, Galkowski, Jeffrey
We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold $(M,g)$ of dimension $n$, let $\Pi_\lambda$ denote the kernel of the spectral projector for the Lapl
Externí odkaz:
http://arxiv.org/abs/2010.03969