Abstract
ABSTRACTLet M be a compact manifold with or without boundary and H⊂M be a smooth, interior hypersurface. We study the restriction of Laplace eigenfunctions solving to H. In particular, we study the degeneration of u|H as one microlocally approaches the glancing set by finding the optimal power s0, so that remains uniformly bounded in L2(H) as h→0. Moreover, we show that this bound is saturated at every h-dependent scale near glancing using examples on the disk and sphere. We give an application of our estimates to quantum ergodic restriction theorems.
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