72 citations · 139 across the 21 of their papers we have counts for
3 papers · 1 filter
Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions
Matthew D. Blair, Christopher D. Sogge
We use Toponogov's triangle comparison theorem from Riemannian geometry along with quantitative scale oriented variants of classical propagation of singularities arguments to obtai…
Refined and Microlocal Kakeya-Nikodym Bounds of Eigenfunctions in Higher Dimensions
Matthew D. Blair, Christopher D. Sogge
We prove a Kakeya-Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors and extends it to higher dimensions. As in the prior work, the key intermed…
-bounds on spectral clusters associated to polygonal domains
Matthew D. Blair, G. Austin Ford, Jeremy L. Marzuola
We look at the bounds on eigenfunctions for polygonal domains (or more generally Euclidean surfaces with conic singularities) by analysis of the wave operator on the flat Euc…