101 citations · 496 across the 72 of their papers we have counts for
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Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary
C. D. Sogge, S. Zelditch
We prove that the Cauchy data of Dirichlet or Neumann - eigenfunctions of Riemannian manifolds with concave (diffractive) boundary can only achieve maximal sup norm bounds if th…
Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
Matthew D. Blair, Christopher D. Sogge
We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving…
Concerning resolvent estimates for simply connected manifolds of constant curvature
Shanlin Huang, Christopher D. Sogge
We prove families of uniform resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean s…
A note on -norms of quasi-modes
Christopher D. Sogge, Steve Zelditch
In this note we show how improved -estimates for certain types of quasi-modes are naturally equaivalent to improved operator norms of spectral projection operators associated…