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Matthew Blair, RLM 10.176: Logarithmic improvements in L^p bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature
Wednesday, January 23, 2019, 01:00pm - 02:00pm
We consider the problem of determining upper bounds on the growthof L^p norms of eigenfunctions of the Laplacian on a compactRiemannian manifold in the high frequency limit. In particular,we seek to identify geometric or dynamical conditions on themanifold which yield improvements on the universal L^p boundsof C. Sogge. The emphasis here will be on bounds at the so-called"critical exponent" where one must rule out a spectrum of scenariosfor phase space concentration in order to obtain an improvement.We then discuss a recent work with C. Sogge which shows thatwhen the sectional curvatures are nonpositive, then there isa logarithmic type gain in the known L^p bounds at the criticalexponent.
Location: RLM 10.176

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