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On the lower bound of the inner radius of nodal domains

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

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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: http://hdl.handle.net/21.11116/0000-0004-40FE-6
Abstract
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.