Publications (48)
Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
Matthew D. Blair, Christopher D. Sogge
On Kakeya-Nikodym averages, $L^p$-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions
Matthew D. Blair, Christopher D. Sogge
Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles
Jason Metcalfe, Christopher D. Sogge
On multilinear spectral cluster estimates for manifolds with boundary
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge
Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation
Hart Smith, Christopher D. Sogge
Averages over curves with torsion
Daniel Oberlin, Hart Smith, Christopher D. Sogge
Global existence for nonlinear wave equations with multiple speeds
Christopher D. Sogge
Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains
Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge
On integrals of eigenfunctions over geodesics
Xuehua Chen, Christopher D. Sogge
Improved critical eigenfunction estimates on manifolds of nonpositive curvature
Christopher D. Sogge
On the $L^p$ norm of spectral clusters for compact manifolds with boundary
Hart F. Smith, Christopher D. Sogge
Riemannian manifolds with maximal eigenfunction growth
Christopher D. Sogge, Steve Zelditch
On Abstract Strichartz Estimates and the Strauss Conjecture for Nontrapping Obstacles
Kunio Hidano, Jason Metcalfe, Hart F. Smith +2
Remarks on global solutions for nonlinear wave equations under the standard null conditions
Hans Lindblad, Makoto Nakamura, Christopher D. Sogge
The Strauss conjecture on Kerr black hole backgrounds
Hans Lindblad, Jason Metcalfe, Christopher D. Sogge +2
Weighted Strichartz estimates and global existence for semilinear wave equations
V. Georgiev, Hans Lindblad, Christopher D. Sogge
Nonlinear hyperbolic equations in infinite homogeneous waveguides
Jason Metcalfe, Christopher D. Sogge, Ann Stewart
Negative results for Nikodym maximal functions and related oscillatory integrals in curved space
William Minicozzi, Christopher D. Sogge
Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge
Hyperbolic trapped rays and global existence of quasilinear wave equations
Jason Metcalfe, Christopher D. Sogge
A natural lower bound for the size of nodal sets
Hamid Hezari, Christopher D. Sogge
Global Strichartz estimates for nontrapping perturbations of the Laplacian
Hart Smith, Christopher D. Sogge
Strichartz estimates for Dirichlet-wave equations in two dimensions with applications
Hart F. Smith, Christopher D. Sogge, Chengbo Wang
On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature
Christopher D. Sogge, Steve Zelditch
Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition
Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge
Concerning $L^p$ resolvent estimates for simply connected manifolds of constant curvature
Shanlin Huang, Christopher D. Sogge
Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions
Yi Du, Jason Metcalfe, Christopher D. Sogge +1
On Strichartz estimates for Schrödinger operators in compact manifolds with boundary
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge
Problems related to the concentration of eigenfunctions
Christopher D. Sogge
Lower bounds on the Hausdorff measure of nodal sets II
Christopher D. Sogge, Steve Zelditch
Kakeya-Nikodym averages and $L^p$-norms of eigenfunctions
Christopher D. Sogge
Strichartz estimates for the wave equation on manifolds with boundary
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge
On Global existence for nonlinear wave equations outside of convex obstacles
Marcus Keel, Hart Smith, Christopher D. Sogge
Concerning the $L^4$ norms of typical eigenfunctions on compact surfaces
Christopher D. Sogge, Steve Zelditch
Lower bounds on the Hausdorff measure of nodal sets
Christopher D. Sogge, Steve Zelditch
Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions
Matthew D. Blair, Christopher D. Sogge
Estimates for the Dirichlet-wave equation and applications to nonlinear wave equations
Christopher D. Sogge
Concerning the Wave equation on Asymptotically Euclidean Manifolds
Christopher D. Sogge, Chengbo Wang
About the blowup of quasimodes on Riemannian manifolds
Christopher D. Sogge, John A. Toth, Steve Zelditch
Global existence for Dirichlet-wave equations with quadratic nonlinearties in high dimensions
Jason Metcalfe, Christopher D. Sogge
Concerning Nikodym-type sets in 3-dimensional curved spaces
Christopher D. Sogge
Almost global existence for some semilinear wave equations
Markus Keel, Hart Smith, Christopher D. Sogge
Eigenfunction and Bochner Riesz estimates on manifolds with boundary
Christopher D. Sogge
Lower bounds for interior nodal sets of Steklov eigenfunctions
Christopher D. Sogge, Xing Wang, Jiuyi Zhu
Global existence of null-form wave equations in exterior domains
Jason Metcalfe, Christopher D. Sogge
Localized $L^p$-estimates of eigenfunctions: A note on an article of Hezari and Rivière
Christopher D. Sogge
A few endpoint geodesic restriction estimates for eigenfunctions
Xuehua Chen, Christopher D. Sogge
On $L^p$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds
Jean Bourgain, Peng Shao, Christopher D. Sogge +1