Lower bounds for nodal sets of eigenfunctions. (English) Zbl 1238.58020
The authors consider the eigenvalue problem of the Laplace operator on a smooth closed Riemannian manifold. In particular they study lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.
Two useful references in this spirit are the following:
1) S.-T. Yau [Open problems in geometry. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 1, 1–28 (1993; Zbl 0801.53001)];
2) M. Craioveanu, M. Puta and Th. M. Rassias [Old and new aspects in spectral geometry. Mathematics and its Applications (Dordrecht). 534. Dordrecht: Kluwer Academic Publishers. ix, 445 p. (2001; Zbl 0987.58013)].
Two useful references in this spirit are the following:
1) S.-T. Yau [Open problems in geometry. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 1, 1–28 (1993; Zbl 0801.53001)];
2) M. Craioveanu, M. Puta and Th. M. Rassias [Old and new aspects in spectral geometry. Mathematics and its Applications (Dordrecht). 534. Dordrecht: Kluwer Academic Publishers. ix, 445 p. (2001; Zbl 0987.58013)].
Reviewer: Themistocles M. Rassias (Athens)
MSC:
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
Keywords:
eigenfunctions; Riemannian manifold; Laplace operator; nodal sets; Hausdorff measure; lower bounds; ballReferences:
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