Lower bounds on the Hausdorff measure of nodal sets II
By Christopher D. Sogge, Steve Zelditch. 2010
75 citations recorded by the source corpus.
We give a very short argument showing how the main identity from our earlier paper (Sogge and Zelditch, 2011) immediately leads to the best lower bound currently known (Colding and Minicozzi II, 2011) for the Hausdorff measure of nodal sets in dimensions $n\ge 3$.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b546a848f26d2a88855a333874db42d724e94f94
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure (2016, result): “See also [4], [5], [19], [7] for the previous results on the lower bounds, which will be further improved in [14].”
- Nodal sets of Laplace eigenfunctions: estimates of the Hausdorff measure in dimension two and three (2016, unknown): “The two known approaches are: (1) follow the ideas of Donnelly and Fefferman and find many balls on the wave-scale λ−1/2 with bounded doubling index, as it is done in [2] or (2) use the Green formula 2 ∫ Eλ |∇Muλ| = λ ∫ M |uλ| and the estimate ‖uλ‖∞ ‖uλ‖1 ≤ Cλ (n−1)/4, see [16].”
- Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture (2016, result): “See also [1], [2], [13], [3] for the previous results on the lower bounds.”