Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

On the lower bound of the inner radius of nodal domains


Georgiev,  Bogdan
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Supplementary Material (public)
There is no public supplementary material available

Georgiev, B. (2019). On the lower bound of the inner radius of nodal domains. Journal of Geometric Analysis, 29(2), 1546-1554. doi:10.1007/s12220-018-0050-2.

Cite as: https://hdl.handle.net/21.11116/0000-0004-40FE-6
We discuss the asymptotic lower bound on the inner radius of nodal domains that arise from Laplacian eigenfunctions \varphi _{\lambda} on a closed Riemannian manifold (M, g) . In the real-analytic case, we present an improvement of the currently best-known bounds, due to Mangoubi (Commun Partial Differ Equ 33:1611–1621, 2008; Can Math Bull 51(2):249–260, 2008). Furthermore, using recent results of Hezari (P Am Math Soc, 2016, https://doi.org/10.1090/proc/13766; Anal PDE 11(4):855–871, 2018), we obtain log-type improvements in the case of negative curvature and improved bounds for (M, g) possessing an ergodic geodesic flow.