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NODAL SETS AND GROWTH EXPONENTS OF LAPLACE EIGENFUNCTIONS ON SURFACES
| Content Provider | CiteSeerX |
|---|---|
| Author | Roy-Fortin, Guillaume |
| Abstract | Abstract. We prove a result, announced by F. Nazarov, L. Polterovich and M. Sodin in [NPS], that exhibits a relation between the average lo-cal growth of a Laplace eigenfunction on a closed surface and the global size of its nodal set. More precisely, we provide a lower and an up-per bound to the Hausdorff measure of the nodal set in terms of the expected value of the growth exponent of an eigenfunction on disks of wavelength like radius. Combined with Yau’s conjecture, the result im-plies that the average local growth of an eigenfunction on such disks is bounded by constants in the semi-classical limit. We also obtain results that link the size of the nodal set to the growth of solutions of planar Schrödinger equations with small potential. 1. Introduction and |
| File Format | |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
