EIGENFUNCTIONS AND NODAL SETS

This is a survey of recent results on eigenfunctions of the Laplacian on compact Riemannian manifolds and their nodal sets. It is the write-up of my talk at JDG 2011.

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[86]  S. Zelditch.  LOCAL AND GLOBAL ANALYSIS OF EIGENFUNCTIONS ON RIEMANNIAN MANIFOLDS , 2009 .

[87]  Rui Hu.  Lp norm estimates of eigenfunctions restricted to submanifolds , 2009 .

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[98]  A natural lower bound for the size of nodal sets , 2011, 1107.3440.

[99]  Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch , 2011, 1107.0092.

[100]  On eigenfunction restriction estimates and $L^4$-bounds for compact surfaces with nonpositive curvature , 2011, 1108.2726.

[101]  J. Bourgain,et al.  On the nodal sets of toral eigenfunctions , 2010, 1003.1743.

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[103]  G. Lu,et al.  A geometric covering lemma and nodal sets of eigenfunctions , 2011 .

[104]  Lower Bounds for Nodal Sets of Dirichlet and Neumann Eigenfunctions , 2011, 1110.6885.

[105]  T. Colding,et al.  Lower Bounds for Nodal Sets of Eigenfunctions , 2010, 1009.4156.

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