E. Wyman

activity

20172021

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math.AP2021

Triangles and triple products of Laplace eigenfunctions

Emmett L. Wyman

Consider an $L^{2}$ -normalized Laplace-Beltrami eigenfunction $e_{λ}$ on a compact, boundary-less Riemannian manifold with $Δ e_{λ} = - λ^{2} e_{λ}$ . We study eigenfunction triple products \[ \…

math.AP2018

Improved Generalized Periods Estimates Over Curves on Riemannian Surfaces with Nonpositive Curvature

Emmett L. Wyman, Yakun Xi

We show that on compact Riemann surfaces of nonpositive curvature, the generalized periods, i.e. the $ν$ -th order Fourier coefficients of eigenfunctions $e_{λ}$ over a closed smooth…

math.AP2018

Period integrals in nonpositively curved manifolds

Emmett L. Wyman

We provide an improvement of a half power of log to standard bounds on integrals of Laplace eigenfunctions over submanifolds of codimension 2 or more, where the ambient space is a…

math.AP2017

Looping directions and integrals of eigenfunctions over submanifolds

Emmett L. Wyman

Let $(M, g)$ be a compact $n$ -dimensional Riemannian manifold without boundary and $e_{λ}$ be an $L^{2}$ -normalized eigenfunction of the Laplace-Beltrami operator with respect to the me…