Toponogov's theorem and improved Kakeya-Nikodym estimates...

Chris Sogge
Toponogov's theorem and improved Kakeya-Nikodym estimates for eigenfunctions on manifolds of nonpositive curvature This is joint work with Matthew Blair. Using wave equation techniques and elementary facts from Riemannian geometry, we show that, on negatively curved manifolds, eigenfunctions cannot concentrate near geodesics as measured in $L^2$. From this we obtain improved $L^p$ estimates which complement the sup -norm bounds in this setting obtained by Berard in the 1970s. Time permitting, we shall also discus related...
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